Learn about the game. Play the demo on the Wizards of the Coast (WOTC) website. This will familiarize you with the game and give you a basic idea of the flow and systems at work.Dungeons and Dragons is traditionally played on a tabletop, with paper and dice.The books can get expensive, but the basics are available online for free. The average player does not actually have to purchase anything, as the DM is in charge of creating the game.
Find a dice substitute. Dice are the only material that is required from all players. There is a dice roller at WOTC's site, or you can find a printable paper template and make your own. A pencil with dots on each side makes an inexpensive replacement for six-sided dice.
Make up a character sheet, or use a pre-made one. If you want the traditional DnD-style game, go with dwarves, elves, humans and even half-lings. If you want sci-fi, you can use any sort of aliens you want.
The System Reference Document (SRD) contains the rules of D&D, which are important to consult as you learn to play. Follow the link and scroll to the bottom of the page. Download the Basic Rules and Spells sections.
If you're planning to be the Dungeon Master (DM), get the Monsters and Magic Items as well. Don't worry about any of the other sections for now, they're for advanced players. Be advised: The SRD is not comprehensive, and lacks vital information on subjects like character generation and gaining levels.
Printable character sheets are available here. For most beginners, the 4th Edition Character Sheets will do.
The System Reference Document is a comprehensive toolbox consisting of rules, races, classes, feats, skills, various systems, spells, magic items, and monsters compatible with the d20 System version of Dungeons & Dragons and various other roleplaying games from Wizards of the Coast.
You may consider this material Open Game Content under the Open Game License, and may use, modify, and distribute it.