Before reading this, read Texas Holdem Rules because Omaha is very similar to Texas Holdem. The difference is very little and it is in the number of hole cards dealt to each player: you receive four cards (in Texas Holdem - two). Though the chances to make a hand are higher than in Texas Holdem, there is one peculiarity: you can use ONLY TWO of your hole cards and THREE community cards.
Let's deal with concrete example. Fancy you've been dealt:
And the river looks this way:
You have... no - it's not Four of a Kind as you may think. You have a Flush... you can't use your third queen. You must use only two hole cards. This is important.
In this example you can also have Three of a kind. Another example:
The river:
Here you have only trips: three 7s. You don't have Full House because you can't use four community cards - only three.