Ever since Bill Hicks's death in 1994 at the age of 32, the Texan comic has been subject to a creeping lionisation that has promoted him gradually into the upper reaches of those all-time greatest lists magazines and TV channels love to establish. I personally have never had a great deal of time for Hicks's shouty, hectoring comedy – it's like being trapped in a room with a sociology student who's just drunk a dozen espressos – but this is a really interesting film biography of him, mining the deepest reaches of his childhood and adolescence to produce a thoroughly convincing and detailed portrait.

Film-makers Matt Harlock and Paul Thomas – both British – are lucky that Hicks's family and childhood pals were happy to unburden themselves to camera, and fill in the blanks of Hicks's early years; they're even luckier that they mastered an impressive-looking cut-and-paste animation technique that allows their film to rise above the usual talking-heads-and-snapshots visuals that such films are normally forced to rely on.

Hicks, it turns out, had a fairly unexceptional upbringing in Houston, the child of strict Baptist parents; his main motivation, at the start, was to get the hell away from them. His sometime writing and performing partner, Dwight Slade, tells some sweet little stories about how they discovered the local comedy club as high-schoolers in the 1970s; it was there that Hicks had his first taste of fame, as an unlikely teenage star of the Texan comedy circuit. His early inspirations were Woody Allen and, more revealingly, Richard Pryor; it was on the latter he apparently modelled his ambition to push the comedy envelope whenever possible. But it's one detail that makes sense of Hicks's later self-destruction; he'd never tasted alcohol until he was 21. And when he did, he fell off the wagon, big time. Ironically, the booze was the main weapon in triggering the abusive, pissed-off persona that gave him his subsequent comedy identity.

Harlock and Thomas take us through Hicks's turbulent career: after stand-up success in Texas, he headed off to LA where, like every two-bit John Belushi wannabe, he and Slade tried to get a movie script off the ground. Their script, The Suburbs, never got made; for some never-explained reason, Hicks lost interest. Had it happened, Hicks could have gone global like his idols; instead, he ended up back in Texas hugging a microphone and making the best of it.

This, no doubt, accounts for his status as the comedians' comedian; he was never sullied by Hollywood success, he remained purely a club comic. Harlock and Thomas detail his heart-rending battle with alcoholism, which at first inspired and then impaired his rapport with his audience. Fortunately Hicks's career coincided with the age of the camcorder: there's quite a bit of grainy footage of his hard-stare, high-decibel sermonising to give us a flavour of his live act.

You don't have to be genius, though, to see that by the end it was getting out of hand, and there's a fascinating switch of Hicks's mood in the year before he died. Hicks, as a Texan, was appalled by the Waco siege in 1993, and used it as a focus for his anti-government tirades. You can actually see an American tide turning; the moment where the leftwing rage of the 1970s and 80s morphed into the rightwing libertarian paranoia that is still with us today.

Be that as it may, Harlock and Thomas have done their subject justice; you can understand, if not necessarily applaud, Hicks's pre-eminence among stand-up comics. It makes it all the sadder that David Letterman, one of their own, should have cut Hicks's last TV performance. He didn't deserve it.