The flop is where the hand usually defines itself; as a result, the play on the flop is usually more complicated then the play on the previous and future rounds. Although the following are some guidelines, we won't pretend to have given you everything you need to know here. We could devote five hundred pages to the play on the flop, and still not cover everything. 

The flop is another spot where most bad players lose a lot of money. A key concept here is that when you enter a pot, you should have a pretty good idea of what kind of flop you would like to see. This takes some practice. A 'good' flop is typically one that has improved your hand to top pair or higher, or has given you a flush draw (you have four cards of the same suit) or an open-ended straight draw (you have four cards sequential in rank). That sounds pretty easy but the trick is knowing when the flop might have improved an opponent's hand more than it has improved yours. Unfortunately, you usually won't catch it a 'good' flop. When this happens-and it will happen a lot-you can generally fold the hand and be done with it. For instance: you have A J, and the flop comes something like K 8 7. In this spot your play is usually to check and fold if someone bets. You can't be sure a jack on the turn or the river will give you top pair, and an ace might give someone two pair, since many players will play any starting hand that includes an ace. Also, you're susceptible to others' flush and straight draws even if you do catch an ace or a jack or both. Another example is when you have a hand like 88 and the flop comes 9 Q 2.  You should fold.  You'll see a lot of players who 'marry themselves' to big starting hands, and stubbornly continue on, calling bets and even raises, when the flop has missed them completely. Don't become one of them.  Remember that one of the basic concepts to playing hold'em successfully is to lose as little money as possible when you do not have the best hand.  People who often 'chase' (keep playing with the hope that their miracle card will come on the turn or river) are not consistent winners.

That said, there are spots where you might decide to stick around to see the turn. For instance, if you have A J and the flop had come 9 6 3, you might call one bet in order to see the turn. The reason is that although the flop did not do much to help your hand, it probably didn't do much to help anyone else's hand either.  An ace on the turn will probably give you the best hand (although beware of someone playing a hand like A3, since an ace will help them more then it helps you), and it's unlikely that a jack will give someone two pair, unless they're playing precisely J9. Further, you can catch 'running' clubs (a club card on both the turn and the river) to give you the best possible flush.

Whenever you've 'missed' the flop (and by that we mean you've neither flopped top pair or better, nor a four flush or an open ended straight draw) and are considering whether or not to continue with the hand, you should ideally decide which cards will likely help you more than they'll help your opponents(s) and calculate the chances of one of those cards landing on the turn. Consider this: each card has roughly a 2% chance of showing up at any given time, so the calculations aren't hard. For example, let's say you have AK and have missed the flop (no A or K). If you think an A or a K on the turn will give you the best hand, multiply 6 (the number of A's and K's remaining in the deck) by 2 (the chances that either of these six cards will drop on the turn). Hence, you have about a 12.5% chance of improving your hand on the next card. These odds may not sound great to you, but as long as there are seven bets in the pot it would be correct for you to call.   Since 12.5% the same as 7:1, you need around seven bets in the pot to justify the call. If you also have 'running flush' possibilities (as is the case with the above mentioned A J), you can usually safely add 1 'out' to the list of cards you'd like to see. An out is a card that will give you the best hand. So, instead of having six 'outs', you would have seven.  You can use these same calculations on the turn when deciding if you should continue on and see the river.

Calculating your odds of getting the cards you want and weighing those odds against how much money you can expect to win if you do end up with the best hand is a whole subject on its own.  If you decide you want to get really serious about the game, it is a concept you should learn.  Or, if you like odds and math, this concept might appeal to you.  For a discussion of the topic of 'Pot Odds", we recommend you read the article Pot Odds 101.  Additionally, the Pot Odds Calculations Cheat Sheet is an invaluable tool.