You have very little control over the cards that are dealt to you and those that appear on the board, but you do have complete control over which cards you choose to play. If you only play good starting hands then you give yourself a better chance of success in the game. No matter how hard you try, you cannot turn bad cards into good ones. The selection of starting hands is probably the single most important area of the game as it is completely within your control, unlike all the other areas.
Do not fall into the trap of trying to turn losing cards into winners. Successfully bluffing someone who has a better hand is possible and a delight to watch when you get away with it but all too often you will be found out and it will cost you chips and so this is a very overrated part of the game.
Generally the rivals you encounter at a table on the Internet are a little looser or wilder than in real life games which means they tend to play weaker starting hands. The best way to play against these types of players is to ensure that you play better starting hands than them. If you can do this, you will automatically win more chips off them than they will win off you, pure and simple! As pointed out above, the best starting hand stand up more often. (This doesn't mean you will always win, just that in the long term you will do better).
Having looked down at your hole cards you must decide what you are going to do. If you're not going to play and you're not in the blinds where you have been forced to bet before receiving any cards - you simply fold. If you wish to play, you need to decide what you are going to bet. Your first option is to simply call the big blind which means that you merely put in amount equal to the size of the big blind. If the blinds are 15 and 30 it means that you put in chips to the value of 30. Your other option if playing is to raise, and if this is your preferred action you further need to consider how much you wish to raise.
Before doing this, however, you need to think about how your table is playing. Whilst waiting for appropriate cards to play you should be paying attention and watching your opponents. If your rivals are generally raising and re-raising then there seems little point in your limping in by just calling as in all likelihood someone behind you is going to raise and then re-raise which is going to force you to lay down your hand prior to the flop.
If the opponents are more passive and tend to just call opening callers or bettors then it allows you to play a greater range of hands. This means that you are likely to get to the flop relatively cheaply. Here in lies one of the key aspects of playing no limit tournaments. Namely, you should be watching your opponents and noting how they play. Depending on how your opponents play will impact directly on the kinds of cards you can play.
Another key factor that affects starting hand criteria will also be how many chips you have to play with along with the number of chips your opponents have to put into play against you.
As already mentioned, your selection of which starting hands to play is completely within your own control. To summarize thus far - there are three key factors to consider before deciding to play a hand. The importance of this cannot be overstated as it can mean the difference between either playing a hand for a call, or the same hand for a raise, or even throwing that very same hand away.
1. Your position (relative to your opponents on betting rounds).
2. The aggressiveness/passiveness or style in which your opponents play.
3. The chip stack sizes held by you and your opponents.