Obviously you never want to have a short stack in tournament play, especially NL Hold'em tournaments. Just as obviously, it is going to happen sometimes and I see a lot of players make a major mistake when playing a short stack.
First, determine that you are short stacked. Sure, the standard method is to figure out the number of revolutions of the table that you can make with the blinds / antes etc. This is correct and the best way to figure it. But, I am not talking late in a tournament when these calculations are necessary. Let's get more basic than that.
Let's say that you are in a 9-player SnG and the starting chip stack is 1500. You have lost a couple of decent size pots and are now down to 700 in chips. The blinds are 200-100, no antes yet. What I see happen many times in situations like this OR CLOSE to this, is a player will try to limp in to pots to see a flop or worse, when they do limp in, fold after the flop if they do not hit. You can not do this with this size of stack. Your only play is to push all in. You are committed to any hand you play. Speculative hands are out at this point. The time to play suited connectors is gone, for the most part. Any hand you play, you have to be willing to take all the way.
What happens to many players in this case, is that they just get beaten down to such low levels that even if they do hit a good hand, they are going to get several calls by players experienced enough just to want to put them out. Playing a 700 chip stack into a 350 chip stack is just prolonging the enevitable.
Let's say it is still early and you have 600 in chips and the blinds are 100-50. You are still short stacked and you are just going to get whittled down by limping into hands. Do not try it. The other thing is, having 600 or 800 chips here really makes no difference. In a 9-player SnG you need to double up or get out. Winning small pots at this point should not be your goal. Only by getting all your chips in the middle can you get your stack back to respectability and be a force in the tournament.