Burning Xbox 360 games that you’ve downloaded (from torrent or wherever) using only free software is actually really easy. I’ve got a video I’m going to show you that will explain (while showing you) exactly what to do. All you need to do is go to your favorite torrent site (if you don’t already have one in mind, I’d check The Pirate Bay first and foremost), download the game(s) that you want using torrent, get the necessary DVD-burning software (he recommends ImgBurn, I agree: fantastic software and it’s free, download it here), and get WinRAR here (also free). Then just follow the directions:
Additional Sources and Further Reading
If you’re really into mods you definitely ought to think about getting a book called The Black Art of Xbox Mods
There’s a really long discussion thread/tutorial on how to burn xbox games over at afterdawn.com, definitely worth a look if you need more info or have questions.