Handling continuation bets with non-made hands:

First, you have to put your opponent on a range when he continuation bets. Obviously you are going to consider his original preflop range and his Flop-CBet-% stat. In general, the lower his PFR% and the lower his F-CBet-% stats, the tighter and stronger his cbet range is likely to be.

If you completely missed the flop, your best choice is to just fold unless have a strong read that you can steal with a raise or on the turn. By "completely missed", I mean that you have no overcards and no weak draws.

If you have a strong draw (8+ outs), you can often decide between calling or raising. Remember -- raising with a draw is only profitable if your opponent has a folding range. If your opponent is a calling station or re-raising maniac, just call and see the next card (the good news: you have great implied odds in these situations). Otherwise, raising with your strong draws is a great way to balance the times you raise with a monster hand.

If you have a hand that is between "complete miss" and "strong draw", like a missed AK on a dry board, you'll have use your reads on your opponent. Is this an overbet from a normally passive player with a 40% cbet stat? You can probably fold and pick a better spot. Is this a half-pot cbet from a loose villain that cbets 90%? This could be a good spot for a call, either for value or to setup a steal.

Finally, pay attention to the bet sizes. It is not that rare to find opponents who announce what kind of hand they are holding based on their bet size (ex: 1/2 pot or less for bluffs or weak hands, pot for strong hands).