Holdem is most wide spread in its no-limit form, but is also often played as pot or fixed limit.
The first betting rounds
Texas holdem is usually played with a small and a big blind, two forced bets that are posted before the cards are dealt. When the blinds are posted each player is dealt two cards face down. After that it's time for the first betting round.
When all the remaining players have contributed an equal amount to the pot, the flop is dealt. Three cards are placed face up on the board. These are community cards, which mean that all players are allowed to use them in order to create the best possible five card poker hand.
A second round of betting, in the same manner as the previous round, occurs. This is followed by the turn - a fourth community card dealt face up - and a third round of betting.
The river and the showdown
When the fifth community card, called the river, is dealt, the final betting round takes place.
If more than one player is still in the hand after the betting is finished, there's a showdown.
The player that made the last bet or raise reveals his/her cards first, if all players check the first player after the dealer shows the cards first. The remaining players then reveal their hands clockwise. Players that don't want to (or can't) compete for the pot can choose to muck their hands unseen.
A player can choose to use both or one of the hole cards together with the board cards to create a hand. He/she can also "play the board" - use all the five community cards to create a five card hand. The pot is won by the player with the best five card poker hand. If two or more players have the same hand, the pot is split between them.