Yu-Gi-Oh! stands as one of the most popular card games of all time. The object is to inflict 8,000 points or more worth of damage to your opponent first, using a combination of monsters, spells, traps and special effects. Specific rules vary depending upon the format--tournament rules are more strict than casual games among friends--but the basics remain unchanged.
Yu-Gi-Oh! is a trading card game, which means that thousands of different types of cards are sold in blister packs similar to baseball cards. Each player "builds" a deck using only some of those cards, presumably in a combination that makes maximum use of their in-game effects. Yu-Gi-Oh! cards consist of three different types: monsters (creatures that attack, defend or create some other effect at the behest of their owner), spells (magical abilities that help support the player) and traps (cards that "activate" when a specific set of conditions are met and cause damage to the player's opponent). Every deck needs to have 40 to 60 cards, with no more than three copies of any single card type in the deck (some cards are even more restricted than that). In addition, players may have a side deck of up to 15 cards, which they can use to swap out for cards in their deck in between matches. Generally speaking, you want to keep your deck as small as possible (this allows you to find the cards you need in a given situation more readily).
Players begin by shuffling their decks and drawing five cards apiece to form a hand. A series of six phases determines each player's turn. In the first phase (the Draw Phase), the player pulls one card from the top of his deck. The second phase is the Standby Phase, wherein the effects of certain cards activate. The third phase, Main Phase 1, is where the player plays his cards: he may "summon" a monster from his hand (laying it face up on the card surface), set a spell or trap card, change a monster card's position on the field (to either attack or defend), and/or activate a card's effect. The fourth phase is the Battle Phase, whereby face-up monster cards fight each other on the field; players compare the monster's attack and defense ratings to see who wins and whether the defending player loses life points in the process. A second Main Phase--just like the first--follows the Battle Phase. Finally, during the End Phase, the player announces that his turn is up; certain effects also activate during the End Phase and if the player has more than six cards in his hand, he must discard some until his hand is reduced to six.
You win the game by meeting one of three conditions: reducing your opponent's life points to 0, rendering your opponent unable to draw a card from his deck or activating an effect from a specific card which states that you win the game. Each individual game is known as a duel; players need to win two duels out of three in order to win the match.