I dare anyone to say that figure skaters aren't under a lot of pressure.
It's true that ninety percent of any sport is mental. Your mind is what controls your body, and if your body is prepared but your mind is not, well, the results will probably not be what you hoped for. The key to skating a good program is good, strong mental focus and self-confidence.
One good idea is to have some sort of set routine for the day of competition. Check screws to make sure they are tight enough, check laces to make sure they are not broken (or in immediate danger of breaking), check costume ahead of time in case it needs some last minute repairs, etc. This way, you will know ahead of time that your equipment will not hinder your performance. It's okay to have a few "superstitions" as well, as long as you don't let it get too out of hand. (In other words, understand that there is a fine line between following a routine and being "obsessive compulsive" about it. The routine is supposed to help calm nerves, but this doesn't mean that all is lost if you cannot follow the routine exactly.)
Visualization is also an important technique to learn, both during training and on the day of competition. Close your eyes and imagine yourself doing your routine the way YOU want to do it. Pretend you have a video camera and can focus in on that image of yourself performing at your very best. If you're not shy about it, you might even want to play your music (preferably with headphones so you don't interfere with others doing the same) and move along with it as you visualize your program.
Once you step out onto the ice, focus on the task at hand. Think about what you have to do, and then do it, without agonizing over the performance you have ahead of you. Excessive worrying can easily cause a skater to "psych themselves out," or commit silly errors that they would not have otherwise done in practice. Once you are out on the ice, it's time to let your "muscle memory" take over. Overthinking it all will only get you into trouble.
And most importantly... RELAX AND HAVE FUN!!!