The film opens by introducing us to Matthew McConaughey's Ron Woodruff, generally being a seedy red-neck stereotype. Honestly, I'd never heard of Ron Woodruff (or the idea of Buyers Clubs) so I can't speak to the veneer of "true story" to the film, but he's portrayed as a man who's never really had to think outside very narrow boundaries his whole life. As the film unfolds, he's not only shown to outgrow his prejudices, but also portrayed as a smarter guy than he was ever asked to demonstrate, showing a grasp of detail and organisation that these early scenes show no sign of. So shortly after an accident at work put him in hospital, Woodruff is diagnosed with AIDS and given a month to live, to which he reacts to with denial and drink and drugs, which is pretty understandable.
From there the film charts his initial trajectory from scoring treatment on the Black Market, to developing his own understanding of the shortcomings in that treatment, to his setting up of a "Buyers Club" - a private members club where you paid memberships but got treatments for free as a way of getting around the restrictions on selling unlicensed medicines. Alongside this, the film uses a Jennifer Garners sympathetic doctor to explore the problems with the Federal Drug Administrations licencing and general reaction to early HIV/AIDS treatments, and boy, do they come off looking like a bunch of assholes.
The redemptive arc of Woodruffs personal growth is highlighted by his relationship with Jared Letos turn as Raylon, a transvestite also suffering from the disease. Their relationship is funny and touching, although Raylon does suffer from being a foil for Woodruff's development and doesn't quite manage to be his own character. That said, it's a great performance and important to prevent the film being about "straight guys getting AIDS" which would feel like a disservice.
As a final comment, the other thing that Dallas Buyer Club does is feel strangely breezy for such a serious subject matter. The film doesn't dwell on anything for too long - there are very few big showy "actor moments", or melodrama, which means that these few moments are more powerful, and the film has a propulsive feel to it, moving from incident to incident. It's actually a lot of fun to watch, serious but not ponderous, and an insight into what much have been a difficult and scary time.