Five-card stud is probably the earliest form of stud poker, originating during the American Civil War, but is less commonly played today than /Seven-card stud and other games. It is still a popular game in a few locations such as South Africa (where it is played with a /Stripped deck).
The description below assumes that you are familiar with the general /Game play of poker, and with hand values (both high and low variations). They also make no assumptions about what /Betting structure is used. Unlike seven-card stud, five-card stud plays very well at /No limit and /Pot limit, though /Fixed limit and /Spread limit games are still more common (with higher limits in the later betting rounds). It is typical to use a small /Ante and a /Bring-in.
Play begins with each player being dealt one card face down, followed by one card face up (beginning as usual with the player to the dealer's left). If played with a bring-in, the player with the lowest-ranking upcard must pay the bring in, and betting proceeds after that. If two players have equally ranked low cards, suit rankings may be used to break the tie. If there is no bring-in, then the first betting round begins with the player showing the highest-ranking upcard, who may check. In this case, suit should not be used to break ties; if two players have the same high upcard, the one first in clockwise rotation from the dealer acts first.
After the first betting round is complete, another face-up card is dealt to each player (after a burn card, starting with the player to the dealer's left, as will all subsequent rounds). Betting now begins with the player whose upcards make the best poker hand (since fewer than five cards are face up, this means no straights, flushes, or full houses). On this and subsequent betting rounds, the player to act first may check or bet up to the game's limit. The second betting round is followed by a third upcard to each player and a third betting round, again starting with the player with the best poker hand showing (thus, the first player to act on each round may change). A fourth face-up card and fourth betting round is followed by a showdown, if necessary (it usually won't be--most deals of five-card stud end early when a player bets and gets no calls).
Here's a sample deal. Assume that a game is being played by four players: Alice, who is dealing, Bob, who is sitting to her left, Carol to his left, and David to Carol's left. Alice deals one card face down to each player, followed by one card face up to each player, beginning with Bob and ending with herself. Bob is dealt the 4♠, Carol the K♦, David the 4♦, and Alice the 9♣. Because they had earlier agreed to play with a $1 bring-in, David is required to start the betting with a $1 bring-in (his 4♦ is lower than Bob's 4♠ by suit). He has the option to open the betting for more, but he chooses to bet only the required $1. The bring-in sets the current bet amount to $1, so Alice cannot check. She decides to call. Bob folds, indicating this by turning his upcard face down and discarding his cards. Carol raises to $3. David folds (forfeiting his bring-in), and Alice calls. Alice now deals a second face-up card to each remaining player: Carol is dealt the J♣, and Alice the K♥. Alice's two face-up cards make a poker hand of no pair, K-9 high, and Carol has K-J high, so it is Carol's turn to bet. She checks, as does Alice, ending the betting round. Another face up card is dealt: Carol gets the 3♥, and Alice gets the K♣. Alice now has a pair of kings showing, and Carol still has no pair, so Alice bets first. She bets $5, and Carol folds. Alice wins the pot without a showdown.
The game can be played with low hand values, in which case the best low hand showing starts each betting round instead of the best high hand showing. Also, the highest-ranking card must pay the bring-in if it is played with a bring-in. If played high-low split, the highest showing hand always acts first.
The fifth and final card is dealt face down in some games. Otherwise play is identical (the player who acted first on round three will therefore act first again on round four since no one's exposed hand has changed). This game is described as "one down, three up, one down" or simply "1-3-1", while traditional five-card stud is called "one down, four up".
See /Stud for many more variations.