For the initial deal each player receives four hole cards face down.
At the showdown, a player must use exactly two of their four hole cards along with exactly three board cards (community cards).

Betting Sequence

Small blind and big blinds are posted by the two players to the left of the button.
Initial deal of four cards dealt face down to each player.
First betting round.
Three community cards are dealt face up in the centre of the table. These are known as the flop.
Second betting round.
A fourth community card is dealt face up in the centre of the table, known as the turn card.
Third betting round.
A fifth and final community card is dealt face up in the centre of the table, known as the river card.
Fourth and final betting round.
Showdown to claim the winning hand.

Example Hand 1

Board Cards: Ah-9s-9h-7h-5h

Hole Cards:
Player 1 has Qc-Qd-9d-2c
The best possible hand is Ah-Qc(or Qd)-9s-9h-9d, for three of a kind, Nines, using the Nine hole card and one of the Queens. The player does not have a full house as that would imply using three of the hole cards (two Queens and the Nine), instead of two.

Player 2 has Ac-Kh-7d-3s
The best possible hand is Ac-Ah-Kh-9s-9h, for two pairs, Aces and Nines. The player does not have a flush as he only has one heart (the King) as a hole card, despite the fact there are four hearts on the board, as he has to use two hole cards.

Player 3 has Jh-9c-6h-2d
The best possible hand is a flush with Ah-Jh-9h-7h-6h, using the two hearts in the players hand with the highest three on the board.

Outcome
In this example, the hand is won by Player 3, with an Ace high flush.

Example Hand 2

Board Cards: Jc-Jh-8d-8s-6h

Hole Cards:
Player 1 has Tc-9s-7h-5c The best possible hand is Jc-Jh-Tc-9s-8d(or 8s), for a pair of Jacks. The player can only use three cards from the board so cannot have two pairs of Jacks and Eights. A straight is also not possible as that would require using three of the hole cards.

Player 2 has Ah-Js-9s-2d
The best possible hand is Ah-Js-Jc-Jh-8d(or 8s), for three of a kind, Jacks. The player cannot make a full house as she cannot use all four cards that make the two pairs on the board.

Player 3 has Kh-8h-6c-3d
The best possible hand is 8h-8d-8s-6h-6c, for a full house. Unlike Player 2, Player 3 can successfully make a full house using two cards from his hole cards and three from the board.

Outcome
In this second example, Player 3 wins with a full house.