What are the basic rules of poker? What are the hand rankings?

Most variants of poker satisfy the following definition, but in a home game of course you are free to modify the rules as you see fit.

Poker is a card game in which players bet into a communal pot during the course of a hand, and in which the player holding the best hand at the end of the betting wins the pot. During a given betting round, each remaining player in turn may take one of four actions:

1. check, a bet of zero that does not forfeit interest in the pot
2. bet or raise, a nonzero bet greater than preceding bets that all successive players must match or exceed or else forfeit all interest in the pot
3. call, a nonzero bet equal to a preceding bet that maintains a player's interest in the pot
4. fold, a surrender of interest in the pot in response to another player's bet, accompanied by the loss of one's cards and previous bets

Betting usually proceeds in a circle until each player has either called all bets or folded. Different poker games have various numbers of betting rounds interspersed with the receipt or replacement of cards.

Poker is usually played with a standard 4-suit 52-card deck, but a joker or other wild cards may be added. The ace normally plays high, but can sometimes play low, as explained below. At the showdown, those players still remaining compare their hands according to the following rankings:

1. Straight flush, five cards of the same suit in sequence, such as 76543 of hearts. Ranked by the top card, so that AKQJT is the best straight flush, also called a royal flush. The ace can play low to make 5432A, the lowest straight flush.
2. Four of a kind, four cards of the same rank accompanied by a "kicker", like 44442. Ranked by the quads, so that 44442 beats 3333K, and then ranked by the side card, so that 4444A beats 4444K(*).
3. Full house, three cards of one rank accompanied by two of another, such as 777JJ. Ranked by the trips, so that 44422 beats 333AA, and then ranked by the pair, so that 444AA beats 444KK(*).
4. Flush, five cards of the same suit, such as AJ942 of hearts. Ranked by the top card, and then by the next card, and so on for all five cards, so that AJ942 beats AJ876. Suits are not used to break ties.
5. Straight, five cards in sequence, such as 76543. The ace plays either high or low, making AKQJT and 5432A. "Around the corner" straights like 32AKQ are usually not allowed.
6. Three of a kind, three cards of the same rank and two kickers of different ranks, such as KKK84. Ranked by the trips, so that KKK84 beats QQQAK, and then ranked by the two kickers, so that QQQAK beats QQQA7(*).
7. Two pair, two cards of one rank, two cards of another rank and a kicker of a third rank, such as KK449. Ranked by the top pair, then the bottom pair and finally the kicker, so that KK449 beats any of QQJJA, KK22Q, and KK445.
8. One pair, two cards of one rank accompanied by three kickers of different ranks, such as AAK53. Ranked by the pair, followed by each kicker in turn, so that AAK53 beats AAK52.
9. High card, any hand that does not qualify as one of the better hands above, such as KJ542 of mixed suits. Ranked by the top card, then the second card and so on for all five cards, as for flushes. Suits are not used to break ties.

(* Such matchups are only possible in games where there are wild cards or where community cards are shared, such as Texas Holdem.)

Suits are not used to break ties, nor are cards beyond the fifth; only the best five cards in each hand are used in the comparison. In the case of a tie, the pot is split equally among the winning hands. For a more detailed explanation, see the section on splitting the pot.

Several variations are possible when playing for low. Some games permit the ace to play low and ignore straights and flushes, making 5432A the best possible low, even if it makes a straight flush. Other games just reverse the order used for high hands, making 75432 of mixed suits the best possible low. Still others count straights and flushes against you but let the ace play low, making 6432A best. Note that in most games in which the ace plays low, a pair of aces is lower than a pair of deuces, just as an ace is lower than a deuce.

When a joker is in play, it usually can only be used as an ace or to complete a straight or flush. It cannot be used as a true wild card, for example, as a queen to make QQ43X play as three queens. When playing for low, the joker becomes the lowest rank not already held, so 864AX is played as 8642A, with the joker used as a deuce.

Although true wild cards are rarely seen in a casino, they are a popular way to add excitement to a home game. Wild cards introduce an additional hand, five of a kind, which normally ranks above a straight flush. They can also cause confusion when two players hold the same hand composed of different wild card combinations. The standard rules of poker do not distinguish between such hands, but some players prefer to rank hands using fewer wild cards above less "natural" versions of the same hand.

You may find these comprehensive poker rulebooks helpful:
Caro and Cooke's Rules of Real Poker
Bob Ciaffone's "Robert's Rules of Poker"
Tournament Directors Association (TDA) Rules
2004 World Series of Poker (WSOP) Rules

If you are interested in learning all about online poker in particular, try the Beginners' Guide to Online Poker. It goes way beyond the basics to topics like record keeping software, site integrity, the law and taxes.