Paulant Films has some great information on how to download and rip Xbox 360 games. In these four video tutorials, you'll learn how to hotswap, stealth patch, and burn Xbox 360 games.
In the first video, watch to see how to hot swap or copy Xbox 360 games to ISO format using WxRipper v1.2.
In the next video, see how to disable auto run if you are having troubles hotswapping.
Then, in video three, learn how to stealth patch your Xbox 360 ISO's using AGBX. This works with raw dumps and as an extra reassurance from the downloaded game.
In the last video, see how to finally burn the Xbox 360 game using ImgBurn.