Basically, the guitar has 5 fret buttons on it, a strum flipper, and a whammy bar (and a start and select button). On easy modes, you usually just use single frets (bear with me here, I don't know my guitar speak very well), but as difficulty levels increase, you go into chords, hammer-ons and pull-offs, tempo increases for some of the songs as well. Now some of the songs are easier than others. Franz Ferdiand was mentioned above as one of the greatest, I don't know where that came from, becuase it's one of the easier songs in the game. Here's a ;ist of the songs that are in the game.
http://ps2.ign.com/articles/662/662002p1.html
Opti is right, it's a lot like Amplitude, but with a guitar. For those of you who don't know what that is, then it'd just be easier to think of guitar hero as DDR with a guitar. So when you choose a song, you're taken to a screen, your fret buttons are shown on the bottom of the screen. Notes start coming down and you have to have the corresponding fret buttons held down while you strum the beat that the notes are coming at you. Here's a screen.
http://www.gamerankings.com/htmlpagesscreens/928520.asp?screenid=5
If you hit the correct notes in time, then the guitar part of the song will play, if you miss then it will be replaced with a mess-up noise. usually sounds like a broken string or something. For the longer notes, or power chords i think they're called.., you can use the whammy bar to distort the guitar sound, and certain notes will have "star power". If you hit them you fill up your star power bar (using the whammy bar increases the amount it gets filled). Once filled you can rotate the guitar so it's vertical and it goes into rockstar mode, where you get more points and your character starts doing all kinds of crazy guitar moves and such.
That's the best I can explain the game, and while it may not be a good explanation, you really have to play the game to get it fully. Let me remind anyone that I don't think I'm good at the guitar becuase I'm good at this game (Not to toot my own horn, but I'm pretty damn good
). I know a lot of friends who play the guitar and they all say that the game is completley different than playing the guitar. Even though I'm better at this game than they are I don't think I'm better at the guitar. It's really just the next level of listening to your favorite songs, jamming out to them. I know there are people out there who probably do think that they're badasses at the guitar, but they fall into the same category of people who think they're good at dancing becuase they're good at DDR. I usually ignore those poeple.