While the flop is the time in an Omaha High Low hand that you will get the most information, the turn is important when it comes to the amount of money you will win or lose because the betting limits double.
The same things you do on the flop when deciding whether to proceed apply here. You need to know whether your hand fits the board, if your hand will be the nuts if you make it, how much money you could possibly win, and who your opponents are.
Some examples will best illustrate how to play typical Omaha 8 hands on the turn. For these examples, we are going to say that your hand is A-2-3-4 with the ace suited in spades. You have five opponents. The first player has checked, the second player bet, the third player called, and it is your turn to act.
For the first example, the board is Q-J-6-6 with two spades. You should know what to do here – fold. Even though you have a draw to the nut flush, with the board pairing there is a good chance, even if you hit the flush, that you won't have the best hand. Folding here is what makes the difference between winning and losing players.
In the second example, the board is Q-J-6-5 with three spades. This board fits you very well. You have the nut flush and a low that cannot be counterfeited. There is a strong probability that you will scoop the entire pot. The only way you won't is if the board pairs on the river, in which case you could lose the whole pot. You need to be aware of this possibility and not get too married to your nut flush if the board does pair on the river, but this doesn't mean you should be playing this hand passively. It's certainly the best possible hand at the moment and should be bet and raised liberally.
In the third example, the board is Q-8-5-7 rainbow. You have the nut low, but almost no chance at winning the high. It's possible you could get quartered for the low if someone has A-2, which is a strong possibility, but you have the added benefit of having counterfeit protection. That being said, however, it's probably better to just call here rather than bet or raise.
In the fourth and last example, the board is Q-6-3-9. All you have is the nut low draw. You need to figure out your pot odds and see if it is worth calling any bets to see the river. If the pot is small, the answer is probably no. If the pot is large, then the reverse is true.