ditto what Helen said!! Also make sure you take note of where the start is too!!
Go through the course several times in your head - it's so embarressing and frustrating when you forget the course - speaking from experience also!! Time your warm up - ie. have a general walk trot and canter round for 10mins, then wait until there are about 4 to go infront of you, and then give him a jump so that you jump your last practice jump and can more or less trot straight into the ring
Kind of obvious but walk the course you are going to ride, every corner. It helps you to visualise the turns and approach to the jumps.
Don't panic and rush into the fences let them come to you.
Always smile in the dressage, even if things aren't going well.
one i found helpful was not to compare myself to other competitors e.g don't think 'argh that horse is faster than mine'(in sjumping) cos it'll dent your confidence
The most important tip is to arrive in plenty of time. When you do this you remain calm & unhurried & have time to do everything, tack your horse, warm him up, walk the course etc. Arrive late & you're rushing & it transfers to the horse & everything goes wrong.
never walk a showjumping course with me as you will learn bad habits instead do as I say not as I do! I 'say' walk your corners, walk either on your own or with an instructor. Don't walk round chatting as you will be distracted and what one person may say is a problem will probably be not an issue to you at all but you will think it will be.
dressage wise ALWAYS smile if you are grimacing the judge won't warm to you, make a positive start with a smile and it will rub off! If something does go wrong in a test forget about it and get on with the next movement. If you do that you only lose one set of marks, if you let it affect the rest of the test by stressing you will lose easily a mark per movement which if at the begining on the test is a lot of marks!!
Make sure you know how many jumps are in the course and always jump the last fence, bitter experience! Arrived late, watched 1 person before me while working in, jumped the most perfect round but hadn't done the last, it was performance working hunter and I would have won by a mile!!! Oh and always check you've learnt the right dressage test, it's no fun trying to learn one 5 minutes before you go in!!