Specific types of hands after the flop and how to play them

Monster Hand
It doesn’t happen very often, but sometimes you “flop” a straight, flush, full house or even a quad. You are very likely to hold the best hand. This kind of hand you should bet and raise to the maximum to put more money in the pot. Watch out: even a monster can be beat. A straight can be beaten by a higher straight, a 3-card flush board is dangerous because a 4th card of the same suite might give somebody else a higher flush (unless you hold the ace of that suit), or there might later be a pair on the board meaning the other guy could hold a full house. Do not fear that too much, it will not happen too often and it doesn’t make sense to loose money here because you fear a hand that is rather improbable. If you encounter fierce resistance, though, you want to be careful.
Slowplaying to keep your opponents in the hand is a mistake unless you have a real monster. On the low levels, your opponents tend to call with bad hands anyway, so play these hands aggressively!

Split Two Pair or set/trips
That kind of hand makes your hand a winning hand most of the time. Split Two Pair means both of your pocket cards have paired with the board. A pocket pair plus a pair on the board does not help you very much.
A set has a higher win expectation than trips, because it’s hidden for your opponents – play aggressively!

Top Pair
You have a hand where the highest card on the board pairs one of your pocket cards. You are very likely to have the best hand, but a pair of Jacks can be beaten if the turn card is an Ace, King or Queen. Here you must bet, raise or check-raise to make seeing the next card as expensive as possible for the opposition. Either they fold – then you have reduced the number of opponents that can beat you, or they call, and thus you win more if their hand does not improve. Of course, the higher your top pair is, the more unlikely it is that you will be outdrawn on the turn or river.
Example: You hold Ad Th, flop is Ts 7d 5c. In this situation it is better to have paired your lower card than your Ace. The Ace gives you top pair with the best possible kicker, while if there was an ace on the board instead of the Ten, you still would have to worry about being outkicked.

Overpair
You have a pocket pair higher than any board card. To be played like the top pair.

Monster draws with several Outs
Assume you are holding a hand with 4 suited cards plus four connected cards – that is a monster draw. Take an even more extreme example: you hold Qh Jh, Flop Th 9d 3h: 4 suited cards plus an open ended straight draw plus two overcards = 9+8+6 Outs.
With a total of 23 outs you want to put as much money in the pot as possible.
With any drawing hand that has 10 or more outs you will always want to see the river card

Flush Draw
Here you have 9 outs, giving you a 35% chance to complete your flush on the turn or river. You should take this kind of hand to the river and try to fill the pot. If you hold only one flush card and three flush cards are on the board, somebody else may easily have a higher flush draw, unless you are holding the ace or you hold the king and the ace is on the board. When drawing to a flush, be wary of any pair on the board, because it may mean someone is holding a full house.

Open ended straight draw
You are holding 4 connected cards like J9 with a flop of T83, so every Q and 7 gives you a straight. You have at least 8 outs, maybe even more if you have overcards. Again, you should bet here and take this hand to the river. With two or more flush cards on the board or a pair, be more careful

Gutshot straight draw
This is a straight draw where only one card completes your straight, like J9 with a flop of 873. This hand is worthless in itself, but in a hand where you have other outs like two overcards, it can make a difference to have additional outs to a gutshot. You still may want to play a gutshot when the pot is extremely big (10 Big Bets or more).
There is also a double gutshot like JT, Flop AQ8: every K and 9 gives you a straight, and that means 8 outs which makes it as strong as an OESD

Low/middle pair
A pair with the second or third highest card on the board. Worthless in a hand with multiple opponents, playable against one or two opponents. In this case you may want to call with middle pair, or even bet out. Fold if you get raised.

Low or middle pocket pair
If you hold a pocket pair like 33 and one or more overcards on the board, fold! You are likely to be beaten. That may provoke the question why you would want to play a hand like 22, 33 or 44 in the first place, because you will have overcards on the flop most of the time. The reason is simple: if you hit the flop every once in a while, you will win big, and that justifies the investment to see the flop, except when somebody raises before you and it would be 2 bets to see the flop.

Overcards
You are holding one or two cards that are higher than any card on the board. A tricky constellation. Against multiple opponents you should check/fold this hand, against a single opponent sometimes a semi-bluff will work. But in general this is a weak hand, especially with only 1 overcard.

Backdoor flush draw / Backdoor straight draw
This is a hand where you need two perfect cards on turn and river to complete your hand, like when you hold J9, Flop is 832. This is worthless unless it gives you additional outs if combined with another draw.