It's awfully dependent on

(1) Number of players involved as gabe indicated
(2) Board texture
(3) Read on player(s) (raise-calling range, how they play monster hands vs. draws vs. probe-minreraises, showdowns)
(4) your position
(5) your image at the table (depending on stakes anyway)
(6) Stack sizes
(7) Stakes
(8) Intuition

Probably a few other things I'm missing.

But it's hard to address as a general problem...I will say that at my stakes, most players will use a minreraise to indicate strength...2 pair+. A minority will use it for a draw - but that tends to happen mostly in small unraised (preflop) pots.
So depending on a lot of factors (my chances to improve to a hand that might beat them, reads, other players involved and their action, gut feel) I tend to call the first minreraise and try to put them on a hand based on the board texture and my read on the player. If I am oop, I will probably 50/50 bet vs. check the turn, assuming it's a blank. Bet vs. not has a lot to do with what I put them on (which comes from reads, experience, and board texture).
Sometimes I overthink things in these situations, and lose value ... but I don't tend to pay off all that many better hands either, so it's probably a wash as far as that goes.