In no limit you're either trying to win the pot right then if your hand is vulnerable, see if you're getting good odds to keep drawing, or figure out how to extract the most money when you have a really good hand. Limit is the same.

With this specific situation of umimproved AK, you must know your opponents. Furthermore, in limit, aggression is rewarded in the long run. If you raised preflop with just two other people in, it's almost always correct to bet out if it's checked to you. Even if the flop is 678 of clubs and you don't have any part of it, no matter what position you're in. Worst case you're the first to act and you bet and both call you. If you don't improve on the turn and say the 9 of clubs comes out, get ready to check-fold. If you're in late position, it's almost always correct to keep firing until the end. If you're really certain the other person is going to call your last bet, you might take a free showdown, but I'm liable to go ahead and fire again. You'll find that a lot of people might have just been chasing an ace or a gutshot and they'll throw it away.