The "Squeeze Play" is a highly effective, albeit risky move that all good players have in their repertoire. Through it's inclusion in the ever popular "Harrington on Hold'em" books; you'll see this play being made more and more.
Essentially the squeeze play is a bluff from late position used when there are already two other people in the pot: a bettor, and a caller. The play is made with any two cards, with the most important considerations centred on the two players already in the pot.
The player opening the betting should be a loose aggressive player (LAG), who likes to raise and bet out more than his fair share of pots. Make sure you've spent a bit of time looking at his play and are sure you've correctly tagged him as a LAG player; otherwise this play could be disastrous. Crucially the LAG player must be capable of laying a hand down; the squeeze play shouldn't be attempted on a "maniac" who'll call a big raise with wide starting hand requirements.
The second player who calls the bettor should be a tightish player. You'll have to decide whether this player has a monster hand and is trying to trap the LAG player; in most cases this would be unusual. If the caller did have a monster hand with more people to acting behind him, calling isn't the best move. Even if the second player (caller) has "aces" in mid-position, calling the original bet is not a good idea as you may suddenly have to play a multi-way pot - thereby increasing the possibility of your aces getting cracked. The better play would be to raise the bettor and play the pot heads-up with a monster or just take it down pre-flop. If the second player was in late position a call could be justified from time to time just to randomize your play.
The more likely scenario is that the second player is calling because he has a "good", but not a "great" starting hand. This idea is loosely linked with David Sklansky's "Gap Concept" in as much as someone has entered the pot and is showing strength, therefore a second player will need a stronger hand to call or raise. Since the second player only calls you can assume they have a good hand, but not a premium pair.
Now for your action!
After seeing the bet and the call, you make a very sizeable re-raise with any two cards. The beauty in this move is that it sandwiches the "tightish" caller and puts him to a very difficult decision. The tight player has called the LAG's bet since he doesn't believe he has a premium holding, but by only calling he's signifying that he doesn't hold a premium hand either. Our raise signals to the original bettor that we have a serious hand and want to play a big pot. Not knowing whether the pot will be heads up or not, the original better makes the sensible decision and folds. This leaves the tightish player facing the big raise out of position with a less than premium hand. Being a tight player by nature the player errs on the side of caution and folds!
There are a few considerations that need to be met before you attempt to execute the squeeze play. Typically you should make this move in the latish stages of the tournament against the medium/biggish stacks. The blinds should be relatively large but your raise should leave both players in the pot with some fold equity. Another consideration are the players left to act after you. You don't want to make the squeeze play if there are short stacks still to act; you could be giving them extra value to call and therefore building the pot odds for the other players too. A final consideration is whether or not you should raise all-in pre-flop? If you do get a caller after raising a large proportion of your stack, often the only move you have left is to make a steal playat the flop. Moving all in pre-flop may be a better option.
If used properly the squeeze play is great bluffing move that will win you big pots and keep you alive in a tournament, however since it's become so well known you'll have to pick your spots carefully.
Good luck at the tables!