It's 1976, and a 16-year old kid from southern California named Alfred Yankovic has just come face to face with one of his heroes. Dr Demento is a record collector turned radio personality with a syndicated show specialising in novelty and comedy records – musical satirists from the 1950s and 60s like Spike Jones, Tom Lehrer and Stan Freberg – not to mention a whole lot of Frank Zappa. Demento has come to speak at Yankovic's school, where the teenager hands him a tape of his own music – a couple of joke songs played on accordion and recorded in his bedroom to a portable cassette recorder. The next week, Demento airs one of the songs, Belvedere Cruisin' – a song about the family station wagon – on his show. "It blew my mind," says Yankovic. "It was all the encouragement I needed. I kept making tapes, and he kept playing them."

It's 34 years later, and "Weird Al" Yankovic has made an impressive career out of his after-school hobby. A dozen studio albums have chalked up combined sales of more than 12m, while more thanr 150 song parodies have made "Weird Al" something close to a household name.

His parodies are pretty harmless, kid-friendly fare, mostly concerning food, suburban life or geek culture – the Knack's My Sharona becomes My Bologna, Coolio's Gangsta's Paradise becomes Amish Paradise, and Don McLean's American Pie becomes The Saga Begins, compressing the plot of Star Wars: The Phantom Menace into just over five minutes. Yankovic says he tries to keep his parodies topical, although sometimes the songs find their way to an audience who never knew the original. "The Saga Begins was a hit on Radio Disney, and of course the kids had no idea who Don McLean was – they just liked it because it was funny," he says. "But then, the next year Madonna did a cover of American Pie and the reaction amongst the kids was like," – he punctuates this with one of his big, whooping guffaws – "How come Madonna's doing an unfunny cover of a Weird Al song?"

Dr Demento might have given Yankovic his break, but it was MTV that made him a star. "MTV and I, we grew up together," he says. "When they first started, there weren't a lot of music videos, and they were hungry for product – they would play virtually anything." Yankovic's videos would do a lot with a little, though. 1984's Grammy-winning Michael Jackson parody Eat It is a triumph of low-budget ingenuity, recreating the Beat It video in shot-by-shot detail (Jackson, reportedly, loved it). Equally meticulous is 1992's Smells Like Nirvana, spoofing the lyrical incoherence of Kurt Cobain and co's break-out hit ("Sing distinctly, we don't wanna/ Buy our album, we're Nirvana") with a video filmed on the same sound stage as the Smells LikeTeen Spirit video, with the same janitor, cheerleaders and even some of the same extras.

Much has changed since the 90s, and Yankovic admits the modern entertainment landscape has made his job more difficult. "It's harder to find songs that I would consider mainstream hits, because our whole pop culture is sort of fragmented," he says. "Radio stations are so compartmentalised, MTV doesn't play music videos any more, the charts aren't even a great indication of what people are listening to." YouTube, however, appears to have given his music a new lease of life, with 2006's White & Nerdy – a take on Ridin' by Houston rapper Chamillionaire – registering more than a million views.

Yankovic's first European tour begins next week, thanks to reformed Canadian post-rock collective Godspeed You! Black Emperor, who have invited him to play on their ATP bill in Minehead. Largely unfamiliar with the band, Yankovic is delighted, if someone baffled by the invitation; he wonders if their fandom is ironic, and seems pleased when I tell him they seem like sincere people. "It seems like an odd choice on their part, but I'm extremely grateful they have. But if want to talk about alternative music," he adds, letting off another deafening guffaw, "I guess there's no one out there more alternative than me."

"Weird Al" Yankovic plays Birmingham Academy on Thursday, then tours. Info: tickets.weirdal.com