As you and others have pointed out, there's a myriad of factors to consider in this situation (as in every hand), so I'll share some real general tips. The nice thing about flopping an unbeatable hand or practically unbeatable hand is that you no longer have to worry about your cards, improving your hand, pot odds or any of that--you're free to turn 100% of your focus to getting inside the mind of your opponent(s), and the effectiveness of which you do this is what will determine how much money you extract. Try to think of all the hands in which you've seen the opponent put in a bunch a chips--how did those hands play out and how can you make this one play out similarly? What's your image in the opponent's eyes? Any history that you have with them can be used as ammo.
At each step in the hand, you should be considering what your move will make the opponent think. If all goes well, you're going to end up putting money in the pot--so do you want to give off the feeling that you're on a draw? that you've got an ok but not strong hand? that you're bluffing?--what would make this opponent put in the most money? You want the whole hand to make sense from their point of view, because when you play as if you have just an ok hand and then end up check-raising all in on the river when they don't see you as someone that makes crazy bluffs, it's going to raise a red flag.
Say you have 6h5h and the flop comes 4h7h8h at a loosish table with multiple players in. Don't be afraid to bet out. Players will come along with a flush draw, two pair, a set, or whatever they think looks good. You're building the pot early and disguising your hand (people usually expect everyone to slowplay a hand like that). On the other hand, if you have pocket 3's on a 10-3-3 flop against one or two people who are pretty tight-passive, it might be better to give them another card or two to improve their hand. Whatever will get the most of their money into the pot.
That brings me to one key point to remember: you don't need to get ALL of your opponent's chips. For most people, they aren't throwing all their money into the middle willy nilly without purpose, so don't think you can magically get them to do it whenever you want it to happen. The goal is to get the MOST out of them. That might mean getting a bet out of a loose player who doesn't like to fold many flops. It might mean setting up someone for a single value bet on the river or an enticement of them making a small bluff (to which they'll fold to your raise). You can lose out on money by getting too fancy and turning it into an all or nothing hand. You want to play this the same way you've played other hands. By doing so, you'll also help yourself in the future. For example, you could play a draw the same way as you did when you flopped that nut full house. A good opponent will notice the similarities and be more likely to fold when you bluff on the river after missing the draw.
One last general tip that I've implemented before is: once the flop comes and you see that you can't lose, make up a imaginary hand (or two) that you'll now play as if you have. For example, when you've flopped that straight flush as above, play the entire hand as if you had the ace high flush draw. If the turn ends up making that a bad plan, think of another hand that would make sense for you to have and continue as if you have that new hand. Another situation could be when you're headsup against a good opponent where there's a long history of being aggressive and bluffing toward each other, imagine having some two specific cards that completely missed the flop but that (imaginarily) you can outsmart him and get him to fold. Play as if that's really what's going on--you're counting on the opponent being good enough to "see through you" and to "outplay" you, when really he's outplaying himself.
Anyways, tl;dr : put yourself in the other player's head, play your hand consistently as if it were some other hand.