There are two things you want to be looking for when looking to continue on the flop. If you have followed the tips of good pre flop play, then you are only getting involved in flops with a much narrower range of hands so you are hitting many flops with the best of it. A great benefit of having a tight image at the table is that often times even when you don’t hit on the flop you can make a continuation bet on the flop and take it down because the other player(s) suspect you have the best hand. You want to use this strategy sparingly, but you definitely want to make use of it because you will not always be flopping monster hands.

Deciding whether or not to make a continuation bet has a lot to do with the board texture, identifying the other players range of hands, and the playing style of the other players involved in the pot. If they are calling stations and will call your bet chasing gut shot straight draws or even with A high and you have not hit the board, then continuation betting makes no sense because you will not get them off their hands and you don’t have a made hand.
Although continuation betting should make up a big part of your flop play, its not always the ideal play if you think you have the best of it and you want to extract more money from your opponents.
For example, let’s say for example you are playing an Ax hand with a high kicker. If the A hits on the flop and you are in early position then it would be a good idea to check raise in this spot. Betting the flop will just get the other player to fold their hand because the A will scare them, but if you let them think that you are weak and check they may consider continuation betting themselves, and you can then re-raise them. They may not be continuation betting with air they could possibly have a draw type hand so you want to make them pay for it to see the turn card.
Another good spot to vary up your play with a check raise is with strong draw hands. If you flop the nut flush and open ended straight draw on the flop, then a check raise in early position would be a good move to build the pot because you have so many outs to improve your hand with. Even if you don’t hit on the turn you can bet the turn and usually take it down.