First things first - the free card isn't actually free, it's half-price! It refers to the practice of raising in late/last position on the flop, when you don't believe you have the best hand, in the hope/expectation that everyone will check to you on the turn, allowing you to check to the river if necessary. It is a very powerful play in Limit poker. When you bet, and especially when you raise, you are indicating strength. There is a natural tendency for people to check to you on the next round, so that they can avoid a second raise. By betting/raising on the flop you are giving yourself the option of 'calling a check' on the turn, where otherwise you might have to call a bet - a bet which is twice the size it was pre-turn!
"It is a very powerful play in Limit poker. When you bet, and especially when you raise, you are indicating strength."
There are a few things to bear in mind:
1) You need to be in late position - preferably last
2) You need to be wary of a check-raise
3) You need to be selective about using this play - i.e. if you consistently try to use this ploy, then people will start check-raising to you.
Playing for the Free Card on the Flop
Lets look at a typical scenario. You hold 
in late position.
The board comes 
.
There are 4 players including yourself, with no pre-flop raises. It is checked to you on the flop. You bet even though you have nothing. You are hoping that either players fold to your aggression (meaning you have bluffed the pot!) or that they will call and check to you on the turn.
If you pick up your straight on the turn by landing the ten (a 1 in 12 chance) you can bet with some confidence. If you pick up the King you very likely have the best hand - because anyone with AK would probably have raised pre-flop, and anyone with JT would have bet, or check-raised on the flop. Your biggest danger there would probably be one of the blinds playing something like K8, but you just can't worry about a hand like that till it is shown to you.
If you pick up a club you have a draw to the second nut flush. If we look at the combined chance of getting a 'good card', then we can see that there are 10 clubs, 3 kings and 4 tens. Even another jack will improve our hand, but then we have to be really worried about anyone with a ten. So, that is 17 cards (20 if we include the jacks) that could help us. We need to 'discount' some of those cards as they may help our opponent more - e.g. someone may have made the nut flush draw, or a flush itself if we get a club, but even still we have something to play for.
The key theme of the 'free card' play is that if we don't pick up what we want on the turn, it is quite likely that everyone will check to us and we can check through to the river in the hope of catching lucky there.
The Free Card Play on the Turn
If your ploy works and everyone either folds or checks to you on the turn, you are faced with a decision. What you do will depend on the 'texture' of the board and also on your 'read' of the other players - what hands are they likely to have played.
Generally speaking if you haven't made your hand, you simply check through to the river and hope to make it there. However, you have to bear in mind that you have now showed weakness and your opponents are quite likely to bet into you on the river. You may however decide at this point to either bet for value (i.e. try to get more money in the pot for those times where you do make your hand), or to try to bluff your opponents out of the pot. It is here that your poker skills will really tell, and there is no shortcut for experience.
If you have made your hand then you want to bet.
Sometimes though one of your opponents will bet on the turn and put you to a decision (see defending the free card below). Your response depends a lot on which turn card falls. If the board has paired, then you may well be looking at trips. If a possible straight or flush card has fallen then that could be your threshold to beat.
Your opponent may even be testing you, or may have gotten lucky and turned two pair or trips. If you have made a hand you are happy with, you might want to raise to define your hand and put him/her back on the defensive. Otherwise you need to look at the odds you are getting and call/fold accordingly.
"Another option is to just call and wait for the turn. Here you would normally then bet out if you make your hand, or check if you don't."
Defending the Free Card
Anytime you allow your opponents through a full round of betting without having to put more money on the table, you are effectively giving them infinite pot odds to draw out on you. Therefore you have to be alive to the possibility that someone is trying the free-card play on you. At the same time, they may have had a legitimate hand and betting back into them may just be giving them a chance to raise (or re-raise) you. If you suspect the ploy is being used, then the best time to take counter-action is usually on the flop, as the bets are still 'cheap', i.e. half-price.
To play back here, you need to have a decent hand, or one with strong drawing possibilities (e.g. AcTc - although with that hand you might well bet for value on the flop). An advantage to this play is that you may be able to trap players in the middle, so that even if you are the underdog, you are improving your chances.
Another option is to just call and wait for the turn. Here you would normally then bet out if you make your hand, or check if you don't. However, you may want to try and bluff if a scare card falls (although this is a very risky play), e.g. if the board pairs and you have an underpair to the board.
Generally speaking however, you just have to make the obvious play - call if you have the pot-odds and fold if you don't. The late position player may be bluffing, or they may have something. That's poker for you, and that's good poker from them - using their position to put 'muscle' on you.
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