How do I play this hand ... ?

I have 88. The flop comes: Q88.
I have one opponent in front of me. I have strong signs that he has Q?.
If the pot is X, how much should I bet here?
The opponents stack is not very big. Should I go all in allready on the turn? How big should his stack be to put him all in on the river instead?

Well if he has a small stack i may check him see if he is gonna bet strong he may if he has that Q if he bets you can then raise him all in see if he calls if not you still stole a few of his chips.

If you have more chips say you have 20,000 to his 2,000(this is not based on any odds ) just push him all in no need to risk all your chips what if he has pocket queens and then 4th street comes and 4 comes out then the river a Q comes out you just risked all your chips when u could have just made him risk his and he won on luck. (chances of that are very slim i know but i have seen stranger things )

What was the preflop action? What limit are we at? Reads on opp?