
To extract the most value when you check-raise with a strong hand, you should do it in situations where your perceived range is wide. For this reason, check-raising on a wet flop will get you more calls than on a dry flop.
For example:

This is a great spot to check-raise for value because you can have a lot of draws in your check-raising range. Whether you check-raise with draws or not in this spot is irrelevant because your opponent doesn’t know. When he faces a check-raise on this board, he is trying to construct a range for you and he will put straight and flush draws in your range. Of course, he will also take into account two pair, sets and straights. But because there are draws in your range, his stack-off range is lighter than if the board was rainbow.
Another reason for check-raising this flop is that there are a lot of turn cards that can slow down the action and prevent you from stacking him. For example, Villain will get it in on the flop with 98, 55, big diamonds, and QQ+. If the turn comes a diamond, a six, a seven, a ten, or a jack, both of you will slow down considerably.
It’s also good to check-raise for balance. This is a great spot to check-raise an opponent who c-bets too much. So, having some nut hands in your range makes Villain more willing to give you credit when you check-raise with a hand such as 77, QJ, and 87.
If you don’t know how to construct a check-raising range, start off with only the nuts in your range and see how your opponent reacts to your check-raise. If you are getting a lot of folds, start adding draws with eight or more outs. If you still get a lot of folds, add some gutshots to your range. If you find that your opponent is calling you light or playing back more often, you can drop draws from your check-raising range and add more value hands such as top pair, good kicker or overpairs that you flatted with pre-flop. The key is to be conscious of what your check-raise means to your opponent and adjust your range accordingly.
A quick example:

Check-raise here with your open-ended, straight-flush draw with overcards 100 percent of the time to maximize your fold equity against a hand like 99. If he calls or shoves, you still have tons of outs. Against aces, you have 54-percent equity. Let’s say you have the same hand but the flop is

Then a check-call is much better because your equity goes way down against top pair. Now, if villain is a NIT and folds to check-raises all the time, then go ahead and check- raise. Although it sucks if he ends up 3-betting the flop, you will get him to fold hands such as QQ-99 and sometimes a hand as strong as K9. However, as a default, I would check-call on this flop.
Important Note: No matter how much information I give you, you have to go out and try it for yourself. By actively thinking about your range in any situation, you will be more aware of your opponent’s range and his tendency. Ultimately, it is up to you as poker player to determine how to fit those pieces together. That comes with practice and observation.