Poker tournaments are an alternative way of playing poker. Instead of betting cash on each hand, you buy in for a certain amount of money, and the whole tournament is then played with that. (A few tournaments allow you to buy additional chips in the early stages.) By the end of the tournament, one person will have won all the chips. The money is then split between that winner, and a few runners up. The runners up are the people who manage to hold onto some chips for the longest.
To make sure that the tournament finishes within a reasonable amount of time, the blinds are gradually increased. This forces players to gamble, since otherwise their chips will be dissipated by the blinds. This also means that falling behind in a tournament puts you in a very difficult position. If the blinds are large, they will take most of your remaining chips. At this point, all you can do is pick a reasonable hand, and bet all your remaining money. You may manage a come-back, or you may be out.
Winning a substantial tournament is going to take a certain amount of luck as well as skill. This means that you should be prepared to gamble a bit more than you would in a cash game—but without being silly about it.
For example, if the game is Hold 'em, and there is not much raising before the flop, it may be sensible to come in with some hands that you would normally fold. By getting to see the flop cheaply, you increase your chances of a big win. You may reduce your average win rate at the same time, but if your luck is merely average, you probably won't win the tournament anyway. You need skill and luck.
Tournaments are typically played no-limit. This means that, if you raise, your bet can be anything between the last bet and all the chips you have in front of you. This adds extra complexity compared to the usual cash game, where a raise is merely a fixed amount.
It is difficult to give good advice about the size of bets in no limit games, because much depends on the players you are competing against. You need to develop a feel for the size of bet that will draw money into the pot, and the size of bet that will push people out.
Suppose the game is Hold 'em, and someone is trying to complete a flush. His or her odds are about one in three. If you are the only person betting against this person, you can make it uneconomical for them to stay in the game. Imagine that there is $10 in the pot, and it is for you to act first. If you bet $1, your opponent has to pay $1 for a one third chance of taking $12. This is a positive return so logically your opponent should call. Now suppose you bet $50. Now your opponent has to pay $50 for a one third chance of taking $110. Notice how it is no longer worth your opponent staying in the game.
Sometimes in no-limit games, you will come across erratic players, who suddenly go all in on mediocre hands. They do this because, usually, everyone drops out so they win a small amount of money. The catch is that they have risked everything for that win.
You deal with these players the same way you handle a loose cash game. If you don't have a particularly good hand yourself, you just drop out. It's frustrating to have to, but you need to wait for your opportunity. When you find yourself with a good hand, you call. You could lose, but that is the risk you take. If you win, you will double your money, which will significantly improve your standing in the tournament.
Why play tournaments?
The attraction of tournaments is that they offer the chance of a big prize. Instead of playing in a cash game, and coming away slightly up or slightly down, a win can be big. This means that the best poker players can get very rich playing tournaments; the World Series of Poker paid a first prize of $5,000,000 in 2004.
The entry fee for the WSOP is $10,000, which is rather a lot to find! However, you can take part in a number of 'satellite' tournaments, where the prize is an entry into the WSOP. Some of these take place offline in casinos, others take place in online poker rooms. Last year's winner, Greg Raymer, won his WSOP entry online in a tournament that cost $40. $40 to $5,000,000 makes it a pretty good investment!