How do I get started with Dungeons & Dragons?

Well, there is a Dungeons and Dragons Starter Set. It comes with a basic version of the rulebook and the GM's guide. Not enough to make your own characters, but it comes with pre-generated characters for you. It gives you the basics on combat, movement, etc. It's more of a boardgame version of the real role-playing game, just enough to let you see if it's something you'd be interested in before you spend a bunch of money on the main game.

The Dungeon and Dragons RPG itself has several books. The main one every player should have is the Player's Handbook, which gives you everything you need to build a character from the ground up and run that character through all the basics.

The DM, or Dungeonmaster needs the DM's Handbook and usually the Monster Manual (if he wants to make his own adventures). Most pre-built adventures have the monster stats for the monsters used in that adventure in the back.

There are also two For Dummies books available to help you get started - Dungeons and Dragons for Dummies and a Dungeon Master for Dummies.