Which competition by the way?
Ahhh, the joys of being a "Dance Mom," if you don't have one, you need to get one. "Dance Mom" = Extrememly helpful lady who knows all about competitions.
Makeup - Depends on your style, if you wear a very dramatic makeup style day-to-day, then you just want to darken it up a little. If you tend to be moderate to little like me, the rule of thumb I was given, "if you don't feel that you look like you should be standing on a street corner, you don't have enough on"

Just remember the judges need to be able to see you smiling across the floor, 15-40 feet away.
Hair - For Smooth, you want it off the neck and for it not to move. Keep it simple and quick to put up. And practice it before hand.
Video - It sounds like they have a company, so you'll want to bring a blank (good quality) videotape, if you go the evening before drop your tape off then. Otherwise, you either need a good friend or time to fill out the sheet, and then stand in line. You'll have to list all the heats you want taped and describe what you are wearing at most. As your first comp, I suggest taping them all, just expect to pay $10-20 a dance. But believe me you'll regret not getting it all. Just be warned, unless you are ballet/jazz trained or seen yourself on videotape dancing before, you are not as good as you think you are, but if you continue this first competition becomes a good psychological tool. And so onto....
Emotions - Emotions will run high. Depending on how high, you may expect a low afterwards. Which sometimes gets worse with the number of competitions you do. Having the first videotape helps, because it gives an indication on how much you've improved and achieved, and takes the focus away from how much you want to improve and how futile it seems.
Gloves and shoes - Make sure to practice in them from here on out. Gloves can be slippery, and shoes need to be broken in/gotten used to heel height, if you aren't already dancing in them.
Time - The biggest thing is give yourself the most time you can inbetween being fully done up and dancing. This allows you to settle down, hopefully get some practice or warmup in. This may be tough if you are dancing in the morning. I've had one competition where I had to be on the dance floor at 7 am. They opened the floor at 6:30. Video showed up at 6:45. Luckily, I already had the tape in.
And lastly...
Look confident and sure and close your feet, and you will do well.
Good luck, let us know how you did.