If you just wanna watch your friend's game and see how he does, no problem. All friends' games will be watchable just by right-clicking their names on your friends list. There's a three-minute delay on the playback, though, so don't try any tricky business. If you're jonesin' for some high-level play, the featured games menu will let you watch the games being played by top-ranked League players around the world. If you wanna analyze their matches, you can rewind, slow down, and fast forward previous footage, allowing you to scrutinize every gank in excruciating detail. Riot Games was nice enough to put together some footage of the new feature in action, as well, so you can check that out right here for the full details.
[Source: Riot Games press release]