NLHE continuation bets
Although you didn't use the term "continuation bet", that's pretty standard for the kind of bet you're referring to here. An example might be if you raise PF with AK and the flop comes J 7 3 rainbow. You can't feel confident that you have the best hand, but you might, and even if someone paired treys or has a pocket pair like sixes, they can't feel confident either, so you're correct to bet to try to take down the pot.
There's no automatic answer about how much to bet, but the general rule of thumb is that you want to act in such a way that an observant opponent can't tell whether the flop could have hit you. ("Hit" for these purposes includes a flop of low cards that preserves the value of an overpair -- in the above scenario, you should play QQ exactly the same way as AK.)
In general, with a good hand you're going to want to bet somewhere between 1/2 pot and slightly more than the pot to deny odds to draws. Therefore your continuation bet should be about the same -- a little more on a highly coordinated flop, a little less on an uncoordinated board.
Standard disclaimer: I'm not a good NLHE player, so more experienced winning players may have something more to say.
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