The first Doonesbury strip, published 40 years ago today, seems naive looked at through modern lenses. It begins with a character so sparsely drawn he barely exists, though you are intrigued immediately by the American football helmet he is wearing while sitting in an armchair.

He is joined by a scraggy-haired young man with a pencil for a nose and the letter O to represent his glasses. This is Michael Doonesbury and the helmeted football player is his new college roommate, BD. Little did their creator Garry Trudeau know when he sketched out that first awkward encounter between them, published on 26 October 1970, that he had just made comic history. Nor did he have any idea that he was embarking on a journey that would stretch into the indefinite future and that those scratchy beginnings would turn into a chronicle of modern times.

The strip had come about almost by chance. Trudeau had been having a bit of fun as a third-year Yale student, dabbling with a sports cartoon called Bull Tales based on a real-life quarterback in the local team called Brian Dowling. Trudeau expected the strip to die at the end of that football season. But the cartoon was spotted by a book editor who thought he'd take a punt on it. Out of the blue, Trudeau, at the tender age of 21, was invited to turn the strip into a syndicated newspaper feature, an extraordinary privilege given the national exposure and the almost tenure-like terms it offered – with contracts lasting 20 years.

"I had given no consideration to a career in cartoons," Trudeau says now. "I thought I was on track to become a graphic designer. So I asked for a one-year contract. My editors howled with laughter."

You could say that was the first Doonesbury joke, and readers have been howling with laughter ever since. And not just laughing. They've been frowning, shouting, crying, blushing – the full gamut of emotions – as a result of a strip that broke the mould of the comic page and shattered countless conventions. Over the last four decades Doonesbury has established itself as so much more than a traditional cartoon. It is a soap opera, a tragedy, a comedy, an investigative agency, a liberal political commentary, a scourge of pomposity and corruption, a humanitarian exercise, all rolled into one.

We are sitting in the east-side Manhattan apartment that Trudeau uses as a studio. I'd expected some scruffy garret quarters, a sort of scraggy-haired bricks-and-mortar equivalent of that first Doonesbury. Instead Trudeau welcomes me into a very light and pleasant space with a wonderful view over Roosevelt Island. The room is richly carpeted and the walls lined with pictures by New York artist David Levinthal. The centre of the room is dominated by a draughtsman's board, on which the latest strip is being crafted.

Trudeau's working day has changed remarkably little in 40 years. He begins it by what he calls "marinating the news", devouring the New York Times, Washington Post and Wall Street Journal at home a few blocks away in the company of his wife, former television journalist Jane Pauley. "Mostly I'm just waiting for something to happen, in me, and mostly it does."

He starts with a subject, and from that the week's offering evolves, produced as a block of six days' strips. The one he's currently working on sees Jeff Redfern in Afghanistan trying to sell the products of his company Overkill to Hamid Karzai. That's pretty typical of what he does, Trudeau says, "taking these highly improbable characters and having them collide with real events".

Trudeau takes me to a back room where volumes of his past work are stored in a cupboard, with his original pencil drawings stacked alongside the inked versions that are done for him by an associate. "In the old days I didn't much value the pencil originals," Trudeau tells me. "So for the first 20 years my Friday ritual would be that as I faxed the last one I would take the six drawings and throw them in the trash can."

Lining this back room are framed magazine covers, six Newsweek and two Time, each one devoted to Doonesbury. That in itself tells a story. When Trudeau began his syndicated cartoon he entered a world where the comics page was almost entirely non-topical and devoid of any political reference.

That was partly the result of logistics – strips had to be drawn six weeks in advance in order to circulate them to newspapers across America – and partly because cartoons were meant to be just that: politics-free, family-friendly fun.

Within a year of those tentative beginnings Trudeau had torn up the rules of the cartoon strip and begun rewriting them, one strip at a time. His work was risque, spikey and above all of the moment. "I was writing about the issues of my day – sex, drugs, rock'n'roll, politics. That was wholly new to comics, which were broad in their humour and rarely touched on anything remotely topical."

Was he aware of what he was doing? "One of the great things of being young is that you're not aware, you lack self-consciousness," he says. "I was wholly clueless about the things I was not supposed to be doing. I didn't set out to be a troublemaker, though quite quickly the strip became a cause of trouble."

That's an understatement. In contrast to his fellow cartoonists, who were busily drawing fluffy animals and naughty schoolchildren, Trudeau waded into Vietnam, Watergate, feminism, abortion, hypocrisy in the White House, pot smoking and sex. Though he himself came from a moderate Republican background, Trudeau found himself manning the barricades of the counter-culture.

"It was the cauldron, the late 60s, when I began to think as an adult. All hell was taking place, the Black Panthers were on trial, students were shot in the Kent State protests, war was waging on the other side of the globe, it was very hard not to be swept up in all of that."

Printers loved him. He pushed his deadlines further and further back, to make the strip more and more live. One printer in Kansas City, Trudeau learned years later, did so much overtime setting his strips that he bought a yacht with the extra earnings and called it Doonesbury.

But editors had kittens. And the owners of local newspapers had fits. Several began cancelling the strip altogether, or censoring its wilder equence in which Zonker extols the virtues of "fine, uncut Turkish hashish" to a young child.

Dozens more dropped the sequence in February 1976 when Andy Lippincott was introduced, the first gay character to appear on the comics page. In November of that year more than 30 newspapers scrapped a four-day tease in which Joanie and Rick Redfern (who later spawned Jeff) end up lying in a postcoital embrace in bed. The Bangor Daily News blocked out that final frame with the weather forecast ("Fair, cold, highs in the 30s").

Censorship was straightforward, and Trudeau never complained because he says "I knew the editors were caught between a rock and a hard place". More sinister was the decision of about a third of the papers that carried him to switch him from the comics to the editorial page alongside their political commentators. "We resisted the move," Trudeau says. "For the simple reason that there are far more readers on the comics page than on the comment page and you want to be where the reader is."

Watergate was the point of no return. Trudeau provoked indignation and adoration in equal measure when his character Mark Slackmayer, a radical DJ, declared Nixon's former attorney general, John Mitchell, "guilty, guilty, guilty!" even before he had been charged. The Washington Post commented sniffily that "If anyone is going to find any defendant guilty, it's going to be the due process of justice, not a comic strip artist."

But the Washington Post hadn't counted on the tenacity and the thick skin of Garry Trudeau. As he wrote on the 25th anniversary of Doonesbury, "Satire is unfair. It's rude and uncivil. It lacks balance and proportion, and it obeys none of the normal rules of engagement. Satire picks a one-sided fight, and the more its intended target reacts, the more its practitioner gains the advantage. And as if that weren't enough, this savage, unregulated sport is protected by the United States constitution. Cool, huh?"

But it must have been scary, I ask him, having such opprobrium thrown at him when he was still so young and so new to the trade.

"Yes I suppose it was. And very distracting. I found myself crisis managing almost as much as I was creating. I made a decision about three or four years into it, that I better step back from giving interviews. Once I did that I found it quite suited me. I found that not having a public profile was not hurting the work, and it freed me up to be the satirist I wanted to be. It also had the unintended consequence of creating a mystique of Trudeau as a hermit, but that wasn't it at all."

Trudeau has maintained that publicity blackout, and with it the mystique of the silent artist, right up to this day. Our meeting marks something of an emergence for him, out of the cave into which he crawled in the 1970s and back into the glare of a public existence.

The reason for his decision to end his almost four-decade-long state of purdah is that he wants to lend his support to a new collection of his work, 40: A Doonesbury Retrospective. The book is a vast tome that runs to 695 pages, yet it contains just 13% of the total strips produced.

Trudeau explains that he and his collaborators decided to focus on the characters and their relationships, rather than the more topical storylines, which in many cases would now have lost their relevance. "There is nothing worse than annotated humour," he says.

The characters resonate over the years, starting with that initial odd couple. Trudeau invented the name Doonesbury by combining doone – boarding-school slang, he says, for "a good-natured dufus, a clueless sort without any mean to them" – with the ending of the name of his friend Charlie Pillsbury. "Charlie was like that, innocent but with a kind of grace, and to my amazement he's been perfectly happy with this association, which just proves he's a doone."

Then there was BD, the original star of Bull Tales. Trudeau's BD was as obtuse and arrogant as the real BD was admirable and self-effacing. Trudeau didn't know Dowling, but much later they met and became friends, and the former quarterback has been supportive of his fictitious namesake.

Such positive feedback was not forthcoming from the model for Duke, the self-obsessed, utterly unscrupulous epitome of evil who has sent a chill down readers' spines for all these years. He was a parody of gonzo journalist Hunter S Thompson, who was deeply resentful of it, seeing his Doonesbury appearance as a form of copyright infringement. Thompson sent an envelope of used toilet paper to Trudeau and once memorably said: "If I ever catch that little bastard, I'll tear his lungs out."

"One never knew quite how seriously to take that, though he did shoot his assistant in later life," Trudeau notes.

Other public figures whom Trudeau targeted were no less undignified in their responses. Donald Trump called him a "jerk" and a "total loser". When Trudeau invoked Frank Sinatra's links with the mafia in an astonishing strip that ended with a photograph of the singer cavorting with his mob friends, Ol' Blue Eyes made the mistake, during a concert at the Carnegie Hall, of attacking not just Trudeau but also his wife – who was a big television sweetheart at the time. "Well, that's the first rule of the neighbourhood, you don't go after the women and children," Trudeau says. "The audience booed him, which must have come as a shock to Sinatra."

The lesson of all this is that when Doonesbury comes calling, do not react, no matter how hurtful the things the strip says about you. It will only make Trudeau redouble his attack if you do. It was funny how few of his victims understood that basic principle, not least the politicians. Dan Quayle, whom he depicted as a feather, wailed that Trudeau had a vendetta against him. George Bush the elder was incapable of not responding, saying he wanted to "kick the hell out of him". Jeb Bush once came up to Trudeau at a Republican convention and cautioned him to "walk softly". "And of course that just encouraged me, I knew I was on the right track. I could never understand why they took it so personally. Satire is a form of social control, it's what you do. It's not personal. It's a job."

Trudeau is now on to his eighth president, who turns out to be one of his hardest. Obama he sees as a "raging moderate"; and satirists don't do well with moderates as "there's not a whole lot to get hold of".

He's also on to the third generation of characters. Doonesbury and BD have both procreated and now, he says, "it's about time for the second wave of characters to have children. That's a frightening thought."

Though the original duo have grown older, they continue to be anchors of the strip. BD led the way into Trudeau's current passion, exploring the traumas and travails of the wounded warrior. It's been Trudeau's device for dealing with the wars in Iraq and Afghanisatan – opposing the wars, yet honouring the men and women who have given everything to them. BD's loss of a leg at Fallujah, followed by his removal, finally, of his helmet, was a poignant symbol of sacrifice. "He had had his helmet on him for 35 years. When it came off it conveyed that he was now vulnerable and his life had changed for ever. I had to figure out who the new BD would be."

So many years, so many characters, so many strips. Fourteen thousand in all. Doesn't he ever fear he will grind to a halt, lose his edge, have nothing more to add? "I try not to permit myself that feeling. It's like climbing a mountain – you don't look down. I don't want to contemplate the possibility too deeply that one week I'll come up blank."

Has that ever happened?

"Oh yes. All the time. Thanks for not noticing."

40: A Doonesbury Retrospective is published today by Andrews McMeel, priced £65. We have five copies to give away. For your chance to win, visit guardianbookshop.co.uk/competitions.