So, someone raises before you act and you wake up with 66. It's not great, but it could be a lot worse. You believe that you're up against an overpair, not two overcards and that your only hope with this hand is if you flop a set. That's only going to happen 11% of the time. It's actually a little less than that, but when you add the 10.78% chance of flopping a set to the .24% chance of flopping quads, you're looking at 11%.

You have to look at the size of your opponent's stack and think about the implied odds. For argument's sake, let's say that he has $100 in front of him and he's going to go all the way with his overpair.

If the raise to you is $10, then if you call:
89/100 times you're going to have to lay it down on the flop= -$890.

11/100 you hit your hand, he goes all in, trying to buy the pot. You call and win = +$1210 (his raise + his stack).

1210-890=$320 in profit. Not bad.

Now say he raises to $30 preflop

89x-30=-2670

11×100=1100

In this case you're looking at a net loss of $1570.

So, it depends a lot on the size of the stack that you're facing. It also changes considerably based on your opponent. If he's very conservative you may make your set and win only a very small pot when he check folds his overpair to you in fear of a set.

My post makes a lot of assumptions and all the math in the world won't help with the human elements of poker. If he raises preflop, you call and the flop comes down AK6, what should you do? Does he have AA, KK, AK, 83? Much of it depends on your reads as a player. If he's very tight and bets out when big cards come, be very careful. If he's like the goofus in my example and will push with just KK to a low board, then you can take his money all day (well 11% of the time.)

So the answer is that it's very relative to stack size and it can get tricky on later streets, but generally speaking I'd call 3-5x the BB and hope for the best. If you don't hit your set, it's an easy laydown…
Unless subsequent bets are small enough to warrant chasing a two-outer.

I've found that most of the time when I flop a set of fours and the other guy goes all in, he's got aces or kings. If he checks, he's got AK and will fold to a 1/2 pot sized bet.

Keep in mind that this stuff I've said is very, very basic and hardly touches the nuances of the game. The fact that you're actually concerned about such mechanics is a very good sign, though, and if you keep on keeping on you'll find yourself a very successful poker player.

Good luck.

Oh, and watch out for me. All too often I've got a set of threes.