Camper vans are great, says Dave Grohl, stretching out in the back of one in a car park in Los Angeles. "Great," he says, "until you have to empty the fucking tank." He means the bit under the in-vehicle toilet, and having mentioned it immediately screws up his face – grimace distorting the mouth-framing goatee, frown sending out ropes of shoulder-length hair from behind his ears. It's not that the 42-year-old musician is imagining having to clear out any sewage himself. As frontman and founder of Foo Fighters (30 million records sold) and the former drummer in Nirvana (biggest indie band of the 90s), Grohl could whistle and be encircled, quickly, by memento-hungry fans only too keen to carry off a vat of his poop; and besides he bribed the rental company with free gig tickets. He won't be emptying any tanks.

No, he is screwing up his face because his five-year-old daughter, Violet, is also on board, almost in hearing range, and he just let slip the f-word. It's a tense moment.

"Daddy?" She is rolling around on a bunk at the front of the van, humming to herself, exploring.

"What-y?"

"I'm going to put my head in the air duct."

"Don't," says Grohl, smirking, "put your head near that air duct," and he mouths to me: That was close. He got away with it. Grohl is good at that.

It is a sunny June afternoon and we are outside one of LA's biggest music venues, the Gibson Amphitheatre, where he and Foo Fighters are rehearsing ahead of a live performance at the MTV Movie awards. The show won't happen for another 48 hours, so Grohl has hired the camper van for some fun with the family – wife Jordyn, daughters Violet and two-year-old Harper. His girls are whey-skinned and very blond, in fancy dress today as fairy princesses, a striking contrast to the tattooed and tanned patriarch, 6ft, bearish, habitually dressed in black.

When he was in his 20s, finding fame with Nirvana, Grohl was skinny, pale and appealingly goofy-looking, a necessary counterweight to the band's tortured, handsome lead singer, Kurt Cobain. Over two decades (a great soupy stretch of time that included the sudden end of Nirvana and then the hurried, sometimes turbulent, ultimately successful formation of a new band), the man has thickened, and pronounced pouches have developed under his eyes. A man-child exuberance remains, however, with Grohl sometimes so involved in his own stories that he gives little childish wiggles of his shoulders to mark the good bits.

"What would Lenny Kravitz think?" he wonders, giving one of these wiggles in his dressing room inside the venue. "What would Lenny Kravitz say if he knew I was turning up to a show like this in a rented van, with my kids?"

Kravitz's name, here, is a random choice – any megastar, especially an uncompromising "find me a hotel that flies!" type, would've made the point. Grohl is worth millions; he has won six Grammys across seven albums and boasts the kind of international pull that brought 170,000 spectators to Wembley stadium over two nights in 2008… And it isn't even a nice camper van. Predominant colour: grey. Interior space: roughly that of a disabled toilet. To Grohl: "Bliss".

His band, he tells me, are "disgustingly domesticated" too. I meet some of them backstage. Once troublemakers and Olympian boozers (10 shots per man the usual pre-show preparation), the Foos have mellowed. In the dressing room guitarist Chris Shiflett has his son clutched in a muscular love-hold as the boy talks of piano lessons. Bassist Nate Mendel sips a beer from the bucket of free drink and tells a story about his family struggles with the sock drawer. The band's big summer tour is only days away (it will include two nights at the 65,000-capacity Milton Keynes National Bowl in July) and Shiflett explains that the extended Foos gang, all the wives and kids, will fly out on the same booked-out aeroplane. Domesticated? Absolutely. But that "disgustingly" might have been Grohl, a gentleman, resisting a boast. They seem very contented.

It's reflected in the music, no longer so raw, so wounded. In the first few years, the Foos' line-up went through a series of lurching and unsatisfying changes as Grohl sought a mix of musicians that gelled; it meant there was lots of frustration to be expended on stage and in the studio. Now Grohl, as lyricist, goes a little heavy on the personal growth metaphor for some tastes, with the new single, "Walk", the one they'll play live for MTV, working over the idea of "learning to walk / learning to talk again". But the band can still startle (as at the end of that song, when Grohl wails frighteningly: "I never wanna die!") and music-buyers have been drinking it up. Their last album, April's Wasting Light, went straight to No 1 in the US and UK charts. They have never been more popular.

"Dude," says Grohl, sipping from a bottle of water and gesturing with it to suggest the crowd expected in two days, "don't think I don't know I could be most of these people's dads. I show up to a gig like this, I'm deaf in my left ear, I have grey hair in my beard. But there's pride there. I've survived the last 20 years in music. I've survived skinny ties. I've survived rap metal."

And before that, he survived the jarring end of "one of the biggest rock bands in the world". He survived the fact that, in the immediate aftermath, he was "a fucking drummer trying to stand up front and play guitar".

"I've survived all of that shit," says the man who in 2011 can still, can still… He searches for an example. "This water," he says, waving the bottle, "I did not pay for this." He gulps it down and opens another. "How rad is that?"

He grew up poor, in Virginia, in a little house with his mother and sister. He was an energetic, mates-with-everyone kid, and even though his father, a political speechwriter, left home when Grohl was six, the family were happy. "Living in a box," his mother has said, "you either get along or you go your separate ways early on. We were OK with it."

"I never needed much," Grohl says, "and I never thought I'd get more than what I had. A trip to Burger King was the biggest thing in the world to me. Heaven." There was no record player at home but his mum, a teacher, could bring one back from school at weekends. Their motto was: it's nice when things are nice.

As a teenager, Grohl made the first feints towards his later life. He self-inked a little "x" on his elbow, the first of many dozen tattoos, and joined a teenage band that performed at local homes for the elderly. ("A bunch of fucking 13-year-olds," he has described it, "playing 'Time is on My Side' to people with oxygen tanks.") He wasn't academic, "destined to work manual labour", and at 17 dropped out of school to become a drummer in a punk rock band called Scream.

In 1990 the band went on tour, and somewhere around Seattle two friends, Kurt Cobain and Krist Novoselic, attended a gig. "He beats the drums like he's beating the shit out [of people's] heads," Cobain would write in his diary, soon after inviting Grohl to join his own band. Grohl was torn: stay with Scream, his pals, or join Nirvana, who at the time were "kind of popular in the underground, and getting a bunch of attention. I called my mother, my rock, one of the wisest people in the world, and asked what to do. She told me there are times in life when you have to do what's best for yourself."

It's nice when things are nice, but "sometimes you just have to be selfish. I took my mom's advice and I'm glad I did." It proved a charmed union. Cobain was flowering as a songwriter and, according to one of the band's early producers, was spurred further in his efforts by the arrival of the knockabout Virginian who hit his drums as if mashing heads. Together the trio recorded an album, and called it Nevermind.

"I remember the first cheque I got," says Grohl, "totally validated me in my father's eyes."

It was a big one. Nevermind sold and sold and sold, pushing the band into the mainstream, sudden success due largely to the album's killer opening track, the seething, wrathful "Smells Like Teen Spirit". That opened with Grohl's unforgettable salvo on the drums, one you couldn't ever hear without miming sticks: bup-BAD-umph, bup-BAD-umph… Playing it live, Grohl used to hunch over his drums to such a degree, leaning into the song, that his forehead almost rested on the snare.

"And my dad was like, 'Don't mess this up, treat every cheque as if it's the last one you're ever gonna make. Because there's no way this is gonna last.' And I was like, I know. This will never last."

There is footage from the MTV awards in 1992 that shows Grohl, loose limbed and giggly, messing about with bandmate Novoselic in an interview. He munches a snack and makes jokes. Interviewed at the following year's awards, in a backstage room at the Gibson Amphitheatre, some serious lassitude has set in. Grohl complains of a "schmooze or lose" culture in music. Beside him, Novoselic suggests that, by accepting money and support from big corporations, Nirvana have lost something essential. "We've sold out," says Novoselic. "Kill us." Cobain, sitting beside him, nods. At the next awards, in 1994, Grohl and Novoselic are shown on their own. "It would be silly to say it doesn't feel like there was something missing," says Grohl, on stage to collect a prize for the band. "I think about Kurt every day." Cobain had shot himself in April that year.

It has become, unquestionably, the thing Grohl is asked about most. Early on he developed stock answers – about Kurt being unable to cope with the complications of fame, about the inspiration he imparted – and Grohl has stuck to them fairly rigidly ever since. I'd assumed that Cobain would be the last subject he'd want to discuss, and I'm surprised, in the dressing room, when he starts talking about his friend unprompted. He tells a story about the days when the band were recording Nevermind, and Cobain went to great efforts to steal a reel from a novelty album by Evel Knievel, the 70s stuntman, which had been recorded in the same Los Angeles studio.

Grohl is in a nostalgic mood, perhaps, because it was 20 years ago to the month that his band recorded Nevermind, in that studio up the road. Only this morning Grohl had finalised a deal to buy the old analogue mixing desk on which the album was made. "Everybody wanted it," he says, drumming his fingers excitedly, "but the owner wanted me to have it. I went to pick it up this morning and almost started bawling." He plans to transfer it to Foo Fighters' own studio, in Northridge, California.

He tells another story. Novoselic was in California recently to play a couple of songs with Foo Fighters, a one-off gig. Grohl, Novoselic and Pat Smears (a current Foo and former guitarist with Nirvana) did a run-through of the set list. After that, they found themselves alone, with time to kill.

"Krist is on bass. Pat's on guitar. I'm on drums," says Grohl (and ridiculously, at this point, my heart starts to thump). "Krist says, 'You wanna run through some oldies?' Me and Pat look at each other. I mean, that's something I've never considered before. I was, like [queasily], 'OK.'"

Which song did you…?

"Krist says, 'Fuck it, let's do "Smells Like Teen Spirit".' And Pat starts playing, and we kick into it. I haven't played that drum beat in 17 years."

How did it feel?

"It was crazy. It was like… a ghost. It was heavy."

Grohl wants to tell a joke – his instinct is to defuse any heaviness – and I want to ask a question. "Our studio manager was the only guy there," says Grohl, going first, "and when we'd finished he was like, 'Hey, you should record that.'" Then I ask my question. Did anybody sing?

"Nobody sang," says Grohl.

Grohl is singing on the MTV stage. "Learnin' to wOWk agay-an!" His foot taps and he flicks his long hair. "Learnin' to tOWk agay-an!"

The stage is… interesting looking. Objects that resemble booms from a boat, made of glass, hang from above, while below parts of the floor have been planted with desert island-like shrubbery. The aesthetic probably has a name, and that name is probably something awful like "decadent shipwreck", but I prefer the judgment of Grohl's two-year-old daughter, who toured the set and was prompted to produce her longest sentence yet: "Daddy's circus is so pretty."

Grohl told me this just before our interview was interrupted, a palm slammed on the door and the singer informed he was needed on set. Grohl was up and out and on to the stage within half a minute, during which time I found myself walking (as if a competition winner, or the cameraman for a soft drink advert) in his wake along corridors, out across tarmac crisscrossed by technicians, then up some steps and through a curtain to the bright lights where the other Foos were already warming up and a roadie was holding out Grohl's guitar. I was almost beyond the drum kit before recalling that no, no, I wasn't a rock musician, quickly backtracking to the wings, and from that vantage, beside a man with a little hose and a pouch of liquid on his back, watering the desert-island shrubbery, I watched the band perform.

"Learning to walk again" serves as a good enough trope for Grohl's travails in the wake of Nirvana's quick collapse. It was never an option, in 1994, for Grohl or Novoselic to continue without Cobain. "So what did I have to lose? I honestly didn't feel I could do anything wrong because I had nothing left."

His only songwriting credit to date had come on a Nirvana B-side, but Grohl (the animal drummer, "the jackass") had quietly been writing his own songs, serious ones, and had about enough to put out a record. No band, yet, but he settled on the name Foo Fighters and released an album with that title in 1995, every instrument on it played by himself. Six albums have followed, including 1999's There is Nothing Left to Lose, recorded in a celebratory mood once Grohl had settled on a line-up of Foos he actually liked, and which won a best album Grammy. Scant years after the collapse of his prospects – "How could I possibly be considered a songwriter after being in a band with Kurt?" – he had become an established frontman in his own right.

Yet Grohl has never quite been able to let drumming go, playing, over the years, in a dizzying number of side projects. "In more bands than chlamydia", as a men's magazine once put it, and all this while befriending everyone in the industry. He worked with Bowie, Diddy, the Bangles; performed with the Prodigy and Pearl Jam; toured with Dylan, recorded with Josh Homme's Queens of the Stone Age, and formed a supergroup, Them Crooked Vultures, with his childhood hero, John Paul Jones of Led Zeppelin. He once told a story about accepting a lift in Coldplay's private plane before realising, minutes into the hours-long flight, "it was all vegetarian food and you couldn't smoke". Last night, Grohl shyly admits, he was out to dinner with Paul McCartney.

"We were talking about musicians who come from humble beginnings," says Grohl (back on the sofa in his dressing room, running his fingers through his hair). "How they're always afraid that everything's going to somehow just stop. Because there's this kind of need for security and stability that doesn't really come with the job, y'know? So you kind of race through this thing, your career, imagining some sort of finishing line – but what will happen when you cross it?" They agreed the thought was terrifying. No wonder musicians go crazy, or get high.

Grohl has anchors, he says, like his family ("my foundation") and the band ("I rely on them and I love them"), and that has allowed him to get by without other crutches. "Weed once in a while, otherwise I stopped doing drugs years ago. But I've watched a lot of my friends continue down that path. Watched them get fucked over by it."

These days the Foos' drummer, Taylor Hawkins, is clean. He's a weather-beaten but smiling 39-year-old in shorts and tennis socks, married with a son: disgustingly domesticated. Back in 2001, however, he was a serious heroin user, and on tour that year he overdosed and was admitted to a London hospital. "I've seen so many people just lose it all with drugs and die," says Grohl, "So I freaked out."

Hawkins didn't die. After two weeks in a coma he woke up, recovery confirmed when he turned to Grohl and told him (as was apparently the band's way) to "fuck off". Grohl had been beside his bed for two weeks. Years earlier, aged 18, Grohl had seen a friend take too much coke and suffer a heart attack in a Virginia car park. Before his death, in 1994, Kurt Cobain had already collapsed in Rome after overdosing on heroin. Grohl, in another country, watched him being wheeled into an ambulance on TV; when he spoke to his friend on the phone he told him: "I don't want you to die." Cobain had only a few weeks to go.

It must feel that he's had to endure this – a helpless view from the fringes – too often. "Absolutely," says Grohl quietly. "When Taylor wound up in hospital I was ready to quit music. Because, to me, it felt like music equalled death. I started praying. I've never been to church in my life, and I'm walking back from Taylor's hospital to our hotel every night, praying out loud in the streets of London. I don't even know if I believe in God. But I felt like, y'know, this is just not right, y'know, what kind of God would let this…"

He catches himself doing a voice, a man-to-the-heavens baritone, and barks out a laugh. He waves a fist at the ceiling, mocking himself, diffusing. Could this instinct to make light of things, I wonder, be what's steered him through? The difference between him and Cobain might only, at root, have been a sense of humour. "I suppose," says Grohl. He thinks about it. No, he decides: it's to do with family. "My mother was a public school teacher in Virginia, and we didn't have any money, we just survived on happiness, on being a happy family. And later, if I ever felt that I was getting swept away by the craziness of being in a band, well, I'd go back to Virginia. Y'know? And I'd spend the night in the room I grew up in. And I'd hang out with people I was in second grade with, and their kids, and 'Uncle Dave's here!', and whatever. I'd have a barbecue with the people I loved, and that kept me from getting lost." He shrugs. "I kept a lot of Virginia in me."

On the MTV set, Grohl's daughters are sitting watching him in the front row, wearing chunky headphones against the noise; now DJ princesses, perhaps, or fairy road diggers. As Grohl runs though his song for the third or fourth time, it occurs to me how strange it must be for them to watch their father go through the bit about his own death. Eyes shut, he roars the lyric, wilder and blurrier – "I never wanna die, Ineverwannadie" – until he's simply screaming a single note into the microphone. Mightn't they find it unnerving?

But then I recall an exchange that Grohl had had with his eldest, back in the camper van. It had come from the Virginia in him, and seemed to say something about the life Grohl enjoys with his daughters.

"Daddy?"

"What-y?"

"When you drive can I sit up front?"

"No. Too dangerous. But you wanna sit on the roof?"

"Yay!"

"No way. While we're driving down the highway? You'd fly right off. But, Violet, you know what we're gonna do?"

"What?"

"After this, we're gonna go to the barbecue store. And we're gonna get a little grill, and some hotdogs, and some hamburgers. And then we're gonna park and we're gonna cook it all up."

"Can we get popcorn?"

"We can get popcorn."

It's nice when things are nice.