I've been studying NL holdem for a while and feel like I can grasp the basic concepts pretty well, but looking at GTO solver play post flop really makes me wonder. When I'm in a spot where I completely missed the flop, I have no idea if I should be betting as a bluff or not. I understand late position is helpful, but what are the other factors to consider in such a situation? Stack sizes?
You should try to think less about the exact hand you have in a particular spot, and think more about the range of hands you can have. E.g. If you are the pre-flop raiser, that means you have a range that includes all the best starting hands: AA, KK, QQ, AK, AQ, etc as well as all the other hands you play, whereas if you just called a raise pre-flop, it's hard for you to have a those strong hands (otherwise you'd have raised). That means that flop that contains high cards favor the pre-flop raiser's range, which means that the pre-flop raiser gets to be very aggressive on these boards. So for instance, say you raise from middle position with 77, and the button calls you. The flop comes AK8. Should you bet? You have an underpair to the flop, which means that if this board hit your opponent in any way, you're behind. But that doesn't matter: You should always continuation bet in this spot, because the flop massively favors your range. Your opponent can't really have AA, KK, AK or even AQ here, because they would have raised those pre-flop, but you can have them.
Now suppose you raise pre-flop from middle position, but this time the flop comes 8c7c5s. What should you do on this flop? The answer is that you should check most of your range, because the flop is much better for the pre-flop caller's range. All those high card hands that you can have that the pre-flop caller is not supposed to have, are now a liability, because while they may very well still be the best hand, you really don't want to bet and face a potential raise with any of them on this board.
Now consider the situation where you raise pre-flop, and the big blind calls you, meaning you will have position on them post-flop. Say the board comes 8c7c6s like above, and the big blind checks to you (as they always should). Should you bet or check behind? Now it becomes a bit more complicated. The answer is that you should continuation bet selectively with a polarized range, i.e. a range that consists of your strongest hands (over-pairs, sets, two-pair), and you weakest draws (low flushes, belly-buster straight draws, back-door flush draws), and you should bet big (close to the size of the pot). With the your medium strength hands (e.g. 98, A7) and strong draws (open-ended straight draws to the nut straight, ace high flush draws, combi-draws, pair + straight or flush draw), as well as you completely hopeless hands (i.e. hands that missed completely and have no chance of improving to the nuts, like 22, A3) you should check behind, because you don't want to have to face a raise with any of them.
what are the other factors to consider
Short answer: everything.
This play is common, so common it has a phrase to describe it; Follow up bet. For many players, it is almost common to do a follow up bet every time they raise, and often players will make a bet when it is checked to them rather or not they raised before the flop.
This is just bluffing and bluffing is often good to do. I personally watch closely when I am in a hand. If it looks good to take the pot with a bet, don't care what my hand is I take a shot. And then I watch more, to figure out if I need to shoot again or cease fire or give him a river to miss his draw. The simplest way I can describe that thought process is that you put the player on the range of hands they have and make a judgement about how likely they are to lay down the hand.
When your doing a bluff, you also need to be watching your own tells. I was once called on a stone bluff by a guy with jack high and lost. I thought the guy was a moron to call the mighty me with jack high, but I am sure there were tells there that gave me away.