One player becomes the dealer, which is indicated by a red button. How this person becomes the dealer is relatively unimportant. Draw straws, or just have someone volunteer. After each hand is played out and won, the dealer button rotates to the left of the current dealer, clockwise.
Before the cards are dealt, the two players to the left of the dealer place two blinds into the pot. The one closest to the dealer posts the Small Blind, and the one to the left of that person is responsible for the Big Blind. The Small Blind is, generally, half of the minimum bet.
Everyone is dealt two down cards, called Hole Cards. The game begins with the player to the left of the Big Blind either calling, raising, or folding to the Big Blind. In a Limit Omaha game, you can only bet the lowest end stakes for the first two rounds.
After the first round of betting is complete comes the Flop. 
The Flop is the first three community cards.After the Flop comes another round of betting.
Once the Flop is down and the betting is completed comes the Turn. The Turn is the fourth community card on the board. Same procedure as the other betting rounds, except you can now bet the maximum stake.
After the Turn comes the last community card, called the River.After all betting is finished, the remaining players reveal their Hole Cards and generally tell the others what their hand is. The person with the highest ranked hand wins.