Leave yourself plenty of time to get there so your horse can settle and you can take it all in and settle down yourself. Go grab a drink, a bite to eat and look over your tests.
If I'm taking a new horse out to a comp for the first time, I like to leave an hour to warm up. I'll lunge lightly first, moving up and down the grounds (if it's early in the morning), then hop on and just walk around for a while on a long rein to take everything in. Then start your warmup.
At home, figure out a good warmup for the comp, so when you get on and start warming up on the day, you know what you're going to work on first.
Some horses need to be warmed up in canter for a while pony club style, others will need to be walked out for a while, asking them to come off the leg, leg yield etc. Work out what your horse needs to work on and find his/her weak points, and warm up accordingly.
Get someone to stand out with you and tell you what looks good, and what you need to fix, even if it's not your coach, it's always good to have eyes on the ground!!
Make sure your up/downward transitions are lovely and crisp, as this will make a great impression on the judge, plus many of the transitions in tests are worth double points, so you want to get them spot on!!
When it is your turn to enter the arena, trot down to the judge, tell them your name and your horses name, make sure they get a look at your bridle number. Have chat to them, get on friendly terms. I like to give the judges a big smile, ask how their day's going and crack a few 'funnies'. If you start off with a positive manner, and get the judges on side, they'll be thinking positively when you enter the arena to star your test, as opposed to the rider who snobs them off!!
STRAIGHT CENTRE LINE!!! I can't push enough how important this is. If you ride down the centre line with determination, dead straight and marching actively forward, the judges will look at you and think you are confident and really know what you're doing. If you back right off down the centre line, make it wobbly and don't establish a nice sharp halt, the judges assume the rest of your test will be the same.
Accuracy is VERY important too. If your horse doesn't have fantastic paces and isn't totally through and working, you will pick up alot of extra marks by riding dead accurate. So many people starting out panic if their horse isn't working as well as they hoped, and focus so much on pulling the horse's head down that they make their cricles look like eggs lol! Just keep your horse forward, accurate and the rest will come.
Don't ride your tests over and over at hom. Your horse will anticipate the movements and not be on your aids at the comp, because he'll think he knows everything!!
If you make a mistake, or stuff up a movement, don't dwell on it. You'll be thinking too much about the past and what you could have done better, when you should be concentrating on the next movement and making it perfect to make up for those lost marks in the last movement.
When you finish the test, even if it was absolutely terrible and you felt like you got 4's for everything, give the judges a big smile and a sharp salute. Don't go out looking angry and upset, and like you want to jump off and belt your horse over the head the second you get out of the arena!!!
Most importantly, best of luck and get plenty of photos!!! Also try to get someone to video your tests for you, then when you get home you can look over them at the same time as looking at your test sheets, and see where the judges awarded you points, and where they took them off so you know what you need to work on most ;)