I've gotten a couple of hits from people searching for that question, and none of the other top ten hits on Google are all that helpful, so in the interest of human knowledge, I'm going to give it a shot.
I'll assume that you (our questing reader) are looking for information on Real Roleplaying, not the computer games by the same name, or, um, the other kind. Not that I don't fully approve of both kinds (better than an FPS at least) but they're really not my area.
So what do you need to start roleplaying? Friends, a place to play, some dice, and a rulebook or two. There are plenty of other optional things various people might add to that list, but that's the core that you need to get started.
Friends You probably have a few of these already, but if you are absolutely starting out with this roleplaying stuff cold, you have have some trouble convincing them to get on board with you. Ask around anyway ("Hey, I found this crazy new game I kind of want to try. Feel like giving it an afternoon?") because there's a good chance you know some people who have secretly always loved roleplaying games but never gotten the chance to play, or, even better, some actual bona-fide roleplayers who are too shy to talk about it with the uninitiated.
If you don't have any friends, or if none of your existing friends are interesting, you have but one option: make some new friends. Go hit up your local game store, check out your school's Magic club, go online and check out the forums. Nearbygamers may be worth looking in to, and there's always Meetup.
If you can, try to get at least three other players, preferably in the range of four or five. The optimal number depends on the system and your particular personality, but having a handful means you can still play when someone can't make it, and let's you build up the kind of banter and player creativity that really makes these games shine. On the other hand, I've heard some very good things about solo games, so if you can only find one or two people, or you'd just prefer a more intimate kind of game, give it a shot.
A Place to Play Either the easiest option or the hardest. Traditional locations are your house or your local game store. If you're still in school, you may be able to start up a club and get some space from your educational facility of choice. (I've always just gone the basement route -- those of you tuning in from home may have some better ideas.) Wherever you play, make sure it's a place you can bring snacks. Soda, chips, and similar items are, again, traditional, though I tend to have more success with cherries, carrots and the like.
Dice Do dice rank above rulebooks? You bet! Even if you're playing a diceless game, or mostly making stuff up as you go, you're going to want something to play with while the other players have the spotlight, and to roll on random charts and such. They're also fun to collect, and for GMs, an excellent way to strike fear into the hearts of your players.
You can go down to your local game store and see what they've got, or buy them online. I'm partial to Chessex myself, but I hear Game Science is pretty much the best in the business quality-wise, and of course you'll need a d30. Check what game you want to play before buying them, since you might need a full D&D set, a bunch of d10s, or a bunch of d6s, but don't listen to those commies that tell you that you can roleplaying with dice you've scrounged from boardgames. It won't be the same.
A Rulebook or Two If you can hook up with some existing gamers, great, get whatever they've got. If you're completely broke you can get away with borrowing their books for a while, but it's nice to have a couple extra copies of whatever books the players reference at the table, and you'll want your own copy to peruse at your leisure. (Carry your books around with you is also a great way to recruit. Especially monster books. People love monster books.)
Starting a group on your own gives you a choice. Which game to start with? Personally, I'd recommend some relative of D&D, since that's sort of the lingua franca of the hobby. Swords & Wizardry and Labyrinth Lord are both simple and either dirt cheap (if you want the dead tree edition) or free (if you download it and print it out yourself).
Ultimately, though, I don't think it really matters what you start out with. If your local game store (or, loathe as I am to suggest it, game section of Borders) has a decent selection, head over and flip through whatever you think looks interesting. If you like a little strategery in your games, you might have fun with 4th Edition D&D, urban fantasy fans should check out White Wolf's offerings, comic book geeks might find Mutants & Masterminds to their taste -- and that barely scratches the surface of games available to day. There's a lot out there.
And that's it. There should be some "how to role play" stuff in the book you get, and some examples of play, but really, as long as you get the basic idea, you don't need a whole lot more. Go make up some stuff that sounds fun.