Your post-flop strategy should be influenced by how you have played pre-flop. You should have a rough idea of your opponents’ range and be evaluating how to get value from your hand. Big pocket pairs unimproved should generally be played strongly on the flop. They decrease significantly in strength on connected boards and are hazardous to play out of position on some flops. Flops like 4-5-6 are obviously going to connect with loose players opposed to tight players.
Folding
Sometimes you will have a big pocket pair and it will be clear that you are crushed. If an incredibly tight player three-bets you then fires a full pot bet on a K-7-4 board, Q-Q is no good. On boards where your hand strength is unclear and your opponents range is almost certainly super strong folding is fine.
Continuation betting
If you had the lead pre-flop, you should continuation bet an awful lot of flops out of position. Say you raised pre-flop with Q-Q and see a A-X-X flop. A Continuation bet here is fine and standard. Check-calling and check-folding are also fine but continuation betting a reasonably strong holding will be the best play.
Checking back
If you are in position, you can check back more hands on the flop, as you are in position and will get to control action on later streets. Let’s imagine you open A-A on the button and a bad regular calls in the blinds. The flop comes 2-2-8 or J-6-3 or Q-9-5. On these boards you want to check to let opponents try and bluff you. Imagine your opponent has K-Q on the 2-2-8 board, he will likely check-fold. Now what happens when you check back and a Queen drops? The trick is to understand your hand strength and the likelihood of an opponent making a better hand when you let one more roll off. So long as you have good post-flop skills, free cards can make you more money.
Facing a raise
Say you continuation bet Q-Q on a 5h-6s-8s board with and face a raise this is player dependant situation too. If the opponent is fairly tight, I’d have no problem folding Q-Q to his raise. If the guy was a LAG, we should have no problem getting the money in here. If the player was a TAG it would be better to call and then get the money in on a non-flush/Ace turn.