I don't play a whole lot of Omaha, but it is basically the same as 7 card stud and Hold'em combined.
Each player is dealt 4 cards face down, there's a dealer button with small and big blinds, and antes may be added further along in a tournament game.
A player "must" use 2 of his/her cards in their hand to form a hand with the community cards or cards dealt on the table.
Betting starts after the blinds are put up, starting after the big blind in a clock-wise direction or from left to right on the table.
(A card is burried before each of the flop, turn and river cards)
After the betting has ended, a "flop" is made with 3 community cards.
More betting is made for the 3 flopped cards.
After the flop betting has ended, the "turn" card is placed up on the table.
More betting is made on the turn card.
After the betting has ended for the turn card, a "river" card is turned up.
This is the final card placed on the table, and final betting is done on the river card.
Remember, only 2 of your hand cards can be played and must be played with the table cards.
If you have a higher pair in your hand than what the table cards show, they will count as playing cards for that round of Omaha.
If 333AK is showing on the board and you have an AK89 in your hand, you would only have trip 3's with AK kickers since that is the highest hand between the board and your hand, using only two of the cards from your hand.
I hope this makes since enough. It can be a bit confusing until you play a few hands.