1) Put together a list of tips for yourself.
For example, you might write down "Stay low" if you tend to stand up too straight. Or you might write, "Relax and have fun." You should refer to this list periodically during the tournament.
2) Decide what your mental frame of mind should be.
Some players get too hyped up for their matches, and so don't play well. Others can't get up for their matches, and also don't play well. Decide where you stand in this spectrum, and either calm yourself down or psyche yourself up before each match. Decide in advance what you need to do. You might prepare differently for each match, based on the opponent's playing style. If you anticipate that you will have to be more aggressive against one opponent, you might have to be more "psyched up" for that match. On the other hand, being hyped up might only make you miss more. You have to decide what works for you.
3) Work on specific strengths and weaknesses.
Everyone has specific strengths and weaknesses that many of their matches are won or lost on. Decide what these shots are, and make sure to practice them both before and during the tournament. For example, if you have trouble with a specific serve, have someone serve it to you over and over - even if you have to pay someone to do it! Similarly, if you have a big strength, such as a forehand smash, make sure to get it going BEFORE the match begins, not when you've already dug yourself a hole by missing the first five attempts.
4) Decide what your actual and working goals are.
For most people, the actual goal is to win. This doesn't mean you aren't there to have fun, but ultimately, most people are trying to win. However, if you go out to a match with this in mind, you might not play your best - you'll be too nervous. Instead, have an "acting goal," i.e. a goal that will maximize your chances of winning. Generally, make "playing your best" your active goal. If you play your best, your chances of winning are maximized, right? You may vary this, however; if you tend to play too passive, for example, your working goal might be to play aggressively.
5) Arrange a warm-up partner and practice routine in advance.
The night before the tournament, arrange who and when you will warm up with. Pick someone who you are comfortable warming up with. This is not the time to practice against someone whose games gives you trouble, or plays what seems to you a "weird" style - that's what you should have been practicing against at the club in the weeks before the tournament. On the day of the tournament, you want someone who can help you groove your shots. Once your shots are grooved and warmed up, you can then adjust to the many wacky styles you may face (as well as more standard ones). Decide in advance what drills you want to do; don't just do forehand to forehand, etc. - make sure to do footwork drills and serve & receive drills. Make sure to either play out points or play some games before you go out for your tournament match - you don't want the first real points you play to be in a tournament match.
6) Bring food & beverages, and eat lightly.
Good food & beverage services at tournament sites are rare. Drink water or bring your own drinks (Gatorade, for example), as well as snacks (such as fruit). Avoid eating a large meal during the tournament unless you have two hours or more free afterwards. It's best to snack regularly on easily digested food (mostly carbohydrates), or you will be somewhat tired while you digest the large meal.
7) Prepare for slippery floors.
One of the most common mistakes I see is not preparing for a slippery floor. Over half of tournaments are played on flooring that is not grippy enough for you to play your best. Many players don't even realize how much they are giving up until they do something about it - and their playing level shoots up. What can you do? There are several options. First, make sure you have good, grippy shoes. Some players even bring two pairs of shoes - one normal pair, and one "extra grippy' for slippery floors. Second, you should always bring a small towel or paper towels to a tournament. If the floors are slippery, dampen the towel, and put it to the side of the table. Every few points, rub your feet on them. Try this, and you'll find it makes a huge difference.
8) Practice your serves.
The day of the tournament, practice your serves. Tuning them up will pay off more for you, time-for-time, than just about any other practice. Yet most players don't warm up their serves before a match, and so don't have their best serves available.
9) Prepare physically.
Prepare your muscles for combat! Before warming up, do some easy jogging to get them warm. Do a thorough stretching routine. Finally, before each match, you might do some short but vigorous physical activity to get the muscles prepared. You might shadow practice, or do a few sprints; however, make sure not to tire yourself out so much that you can't play the match. Somewhat related to this is getting enough sleep in the last few days before the tournament. (I've read studies that have shown that it's actually more important getting enough sleep in the last few days before a sports activity than the actual night before.)
10) Do some meditation and mental visualization.
Let's not get mystical here. However, you will play better if you take some time before a match to clear your mind and do some mental visualization. Go somewhere quiet, and blank your mind out. Then visualize yourself doing the shots you plan on doing. A few minutes of this is worth more than an equal amount of practice time on the table.