When to push:
1. you have the nuts and opp is raising/reraising you

2. you have a draw with numerous outs (i don't give a specific number because it depends on how much you want to gamble.)
2a. I'm putting this point down here because I think it's a finer point to the above. Pushing with fold equity is basically the same as above. The relative strength of your hand gives you the probability to win x% amount of time in that situation. So, pushing with fold equity is when your bet will create a pot (if villian calls) in which the bet amount is equal, or close to equal, to x% meaning you are covering your +EV expectations of winning said pot.

3. you have a read on an opponent ( i.e. will lay down marginal hands against heavy aggression) and you believe he will fold his hand