Tip #1 - When a final table begins, what you do will mostly be dictated by your stack size. If you are short, with say less than 10 big blinds, then you generally have two options. You can either start gambling, looking to double up and put yourself in a better position to win, or you can sit back and try and move up a couple spots to make more money. The option you choose will depend mainly on whether the money matters to you. The best players are the ones where the money matters but they don't let that get in the way of them making the best decisions and going for the win.
Tip #2 - If you have a medium or large stack, there is more you can do. It's not much different than play in the stages that led up to the final table. You want to attack the stacks that you can bust or cripple and avoid massive confrontations with the stacks that can bust you unless you feel you have the best hand. Sometimes a player will shift gears from loose to tight, or tight to loose, now that they have made the final table. If you see that someone is all of a sudden playing differently than how they were previously, make a note of it and adjust.
Tip #3 - It's important at the beginning of the final table to relax and not panic. You've played for hours or days to get to this point and it'd be a shame to let all that good play go to waste. The best thing you can do is to continue to play the same way that got you there with a few adjustments based upon the dynamics of the table.
Tip #4 - Once you are down to five players, you will need to make adjustments for several reasons. The first is the obvious reason that play is shorthanded and the starting hands you play need to be adjusted. The second is in response to other players adjusting their play due to it being shorthanded. It's important to not get tied into hand values and what the normal play in a given situation is.
Tip #5 - When you get down to three handed and heads up play, the two main factors you need to evaluate is your stack size in relation to your opponents and your opponents playing tendencies. The key is to be aggressive and to take advantage of your opponent's tendencies. If you are short, it's important that you don't let your opponent grind you down to nothing. Take some chances to put yourself back into the game.
The Main Holdem Strategy Index: The Great Game of Holdem