One way to play Magic: the Gathering, favored by many as it ensures that the game is about skill and not money, a draft usually involves three or more players (if there are only two of you, I suggest you try a Soloman Draft instead), and they need three 15-card booster packs each, and a good amount of basic land (plains, forest, island, mountain, and swamp) each. Each player opens one pack, examines the cards, chooses one, places it face down in front of him, and passes the rest of the cards in the pack to the player next to him. (Usually, the direction in which cards are passed alternates for each pack, so if you're passing to the right for the first pack, you'll pass to the left for the second pack) Each player repeats the process with the cards that have been passed to him. Cards continue to be "drafted" and "passed" until there are none left from the packs which have been opened, and each player opens a second pack and does the same with it, followed by the third pack.
After all of the packs have been opened and all of the cards have been drafted, each player must now construct a deck of at least 40 cards, composed of the cards he drafted and from the communal pile of basic land. Players may not trade cards with each other, nor may they use any other cards they may own. A time limit is usually imposed during official DCI sanctioned tournament play, but in a casual setting, the deckbuilding time isn't over until all of the players agree that they are ready.
After the decks are built, a series of games is played. One way to do this, for four players, is to pair them off at random, and each pair plays to best out of three (or, if you have the time, best out of five), at which point the winner of each game will play against each other, also to best of three (or five), to determine the overall winner.
Most people play for the cards drafted, that is, the overall winner recieves all of the cards that were in the packs. This, of course, is somewhat risky, with booster packs selling at about $3 each, and a player may come out of the draft with nothing, but it gives everyone some motivation to play better.