Most people just call down. In your decision how much you can call you should read up on pot odds and implied odds. For example if you and the villain are pretty deep, and the villain doesn't bet much and suddenly he overbets the pot - you might not get the right odds to call, but if both your stacks are big enough in relation to the bet, you can make that call because you are much more likely to get payed off if you hit it.

Some players like to minbet into the initial raiser with a draw. Most of the time it goes: check/bet/call on the flop and then he makes a small bet on the turn. This can actually be a good play, because many microstakes players are immediately afraid you might have a hand and go into calldown mode... or they think they're trapping you or whatever. So look out for those situations. Make a note on a player if you see him do that.

There are some situations where you can actively bet draws. If you have 13 or more outs you are actually a favorite to win the hand - you can play those pretty aggressively. I definitely c-bet if I make the nut flush draw. Or in last position in a multi-way pot if nobody is showing strengh. What that also does is that in the case somebody has a smaller FD there, you might get his whole stack if you both hit.

Also don't discount overcard draws. QK on a TJx board is a monster. TJ on a QKx board - not so much.