1. Early in the tournament, don't gamble. You'll see other people around you gambling, but you shouldn't get involved unless you have a big hand. Big hands are AA, KK, QQ, AK. For the first 3-4 blind levels, you shouldn't be playing any other hands except these (with one exception, listed next). If you have AA, KK, or QQ, try to get all-in before the flop. Your preferred plan with AK is to re-raise a raiser all-in and have him fold. If you see a flop with AK and you didn't hit a pair, you probably need to get out.
2. You can call with a pocket pair (e.g., 88) if what it costs you to call is less than about 1/15th of your chips. For instance, if you have 1000 chips, if you can call for less than 60-70 chips, do so. Your plan is to flop a set or an overpair. If you don't flop a set or an overpair, you get out. If you flop a set, try to get all your chips in the middle. If you flop an overpair, you may be willing to get all-in - you may not. Tread carefully.
3. If you're the second person to put in a raise, it's usually not correct to raise the minimum amount. A good rule of thumb is to raise about the size of the pot. For instance, suppose everybody has 1000 chips, and it's 20 to go. One person calls, the next makes it 40. If you have KK, you should not raise to 60. There are a few options here:
Raise the pot. That would be a raise of about 130 chips (including the 10 and 20 chips blinds that are already in).
Raise a large amount that will really commit your opponent to the pot after the flop. For instance a raise to 400-500. When the flop comes down, if there's no dreaded ace, then move the rest of your chips in.
Raise all-in right there. If somebody wants to call you with AJ or QQ, fine.
4. When betting after the flop, your bet must be some reasonable fraction (perhaps not less than 1/3 or 1/2) of the pot. Otherwise, you are giving drawing hands the correct pot odds to call. If they hit their draw, they can now put you all-in. Unless you have an unbeatable monster (for instance, you flopped a full house), it's rarely correct to "suck people in." You want them out.
5. When you make a bet with what you believe to be the best hand, bet enough so that an opponent with the most obvious draw would be making a mistake to call. For instance, suppose you have QQ, and the flop is J-7-3 with two spades. You are concerned about the possibility of a spade flush draw being out against you. The probability of that person hitting a flush is about 20% (one in five times) on the turn card. Make sure you bet more than 1/5th of what somebody could win from you if he hits his flush on the turn.
6. Conversely, don't call with a draw unless you can get the right pot odds. Suppose there are 100 chips in the pot on the flop. You and your opponent each have 800 chips. If he bets 400 chips on the flop and all you have is a flush draw, you can't call - you're not getting the right price.
7. It is almost always better to be the bettor or raiser than the caller. Particularly in all-in situations, you would much prefer to have "fold equity" - that is, your opponent folds and you don't have to have a showdown. So in general, you need a much stronger hand to call all-in than you do to bet (or raise) all-in.
8. If you're going to make a bet or raise, and you will be "committed" to the pot after that bet or raise, then go ahead and put all of your chips in. That is, suppose you and your opponent have 1000 chips each. If you bet 900 before the flop and he calls, there will be (at least) 1800 chips in the pot after he calls. There is virtually no flop that would make it correct to fold for your last 100 chips. So go ahead and bet all 1000 right now. The only time this might be correct is if your opponent will make the analogous mistake. That is, he won't call all 1000 chips right now. But he will call 800 chips now, and then feel obliged to call his last 200 after the flop. If he's that kind of player, it might be a correct play with a huge hand like AA.
9. As you get near the cash, and particularly on the bubble (one more player to bust out before everybody is in the money), many players will become extremely tight and play very conservatively, unwilling to be the last one to bust out before the money. Take advantage of this - you should be able to steal blinds frequently. This will set you up with a good stack once you've gotten into the money.