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Each player is dealt 4 hole cards. A further 5 cards are dealt out on the board (ie flop, turn, river, as in holdem).
You must play exactly 2 cards from your hand, and 3 cards from the board to make your best hand. (This differs from holdem, as remember in holdem you may just play 1 of your hole cards, or even none of your hole cards. You cant do this in Omaha. You must play exactly 2 cards from your hand, no more and no less)
The hand ranking is the same ranking as in holdem, with a royal flush being the best possible hand, followed by any other straight flush, followed by quads etc etc
You bet in rounds as in holdem, being able to bet pre-flop, on the flop, on the turn, and on the river.
Playing exactly 2 cards means that if 4 clubs are on the board, and you have one club in your hand, then you dont have a flush, because you must play 2 cards, not just 1. Similarly you cant play 3 or 4 cards from your hand. It must always be 2 as we have stated above.
Example of playing only 2 cards :- If trips come on the board eg KKK74, then 55QJ wins over A247 (the first hand has KKK55, but the second hand does not have a boat, it only makes AKK77).
Quick List of Good Starting Hands
AAxx
KKxx
QQxx
JJTT
JJT9
AKQJ
KQJT
QJT9
JT98
2 pairs which are 2 suited
You'll figure out a few others through experience