Generally you need to adjust your play from what got you to the final table, in part because of the increased size of the blinds. Plus the payouts increase rapidly as the final table winds down.
If you are short-stacked, you need to be relatively patient and get your chips in the pot when you are likely to have the best hand. Even more important is your position relative to the blinds and your reads on the other players. If you go all in without many chips with the chip leader in the big blind, you better have an A and decent kicker or a pair. If you have enough chips to at least make someone think before calling, then use that to your advantage. Stealing a few blinds or doubling up a time or two will bring you to an average stack in no time.
If you are average-stacked, pay even closer attention to your position and the relative chip stacks around you. If it's folded around to you near the button, don't hesitate to raise with almost anything. But don't be afraid to fold, even a decent hand that might put you out. Don't bet an amount on a marginal hand against a more desparate player that's likely to push all in and cripple your stack. Don't chase flushes or straights against bigger stacks unless you've already represented a made hand.
If you're a chip leader, you need to play aggressively and exert pressure on the average stacks. You also might want to risk some chips to put the smaller stacks out on marginal
hands. If the pace is a little frantic, you can always step aside until a few players are gone. If the play is tentative, you probably should be even more aggressive to set yourself up for the final few players.
My most important rule is "don't be afraid to fold the best hand". There's no shame in waiting for a better opportunity. My second most important rule is "don't panic". For whatever it's worth, I've had pretty good success at final tables. Good luck.