Where in the world have I been?? We have a hunter section on HF??? Very cool!
Ditto everything Maura said. Someone told me Georgina Bloomberg described an idea hunter as a horse that a blind dumb monkey could ride. (something to that degree, I can't remember the quote exactly). And that's the goal, to make everything look as easy and simple as possible. I haven't showed in any eventing shows but I have done many many dressage shows and I noticed that (depending on the comp) if you make one mistake in the test but the rest of it is spectacular you can still be somewhat ok overall. But in the hunters you can have a perfect round and one biff and your score goes down quite a bit. So the challenge is to get 8 perfect distances, get every lead change, get the right number of strides in the line, make good corners, be on the correct speed and never change it for the entire course. Oh, and make it look easy. ;) I would highly recommend getting Judging Hunters and Hunter Seat Equitation by Anna Jane White-Mullin to know what the judges are really looking for.
Insider tips? In a flat class know your competition and your horse. If I'm not on a good mover I try to lay low. But if I'm on a hack winner I make sure that judge can always see me. You won't get penalized for cutting across the ring or making a circle. So if I"m on a horse that's iffy about picking up the correct lead on a straight line I will either make sure i'm in a corner or I cut across so I can "make" a corner. And the flat classes will almost always run the same. (tracking left, w/t/c/w, reverse w/t/c/w line up)
On a course if you get three things right you should generally be ok.
1) Always get the right number of steps in a line. Every once in a while you'll get a judge who will think it's ok for a smaller horse to add but generally a regular sized horse needs to be on a 12 foot stride for a course 3" and under. So for some horses that's a faster pace, some that will be slower. A pony's correct step will be the add. (A small pony is a double add)
2) Get every lead. Trotting (even trotting a simple change) automatically drops your score down to a 50. (From 100) It's a big mistake. :) So if your horse can't do a flying lead change I'd try to get her to land on the correct one. It's better to do a balanced counter canter then to trot a change. But it's slightly better to at least swap in the front then not change at all.
3) Distances! The whole goal is to be smooth. So a chip in or leaving long is at best not smooth, at worst dangerous. This is probably the biggest things a judge is watching. If you look at the judges cards, it's the main thing on there. I've had trips that were 7 perfect distances and one biff and been out of the ribbons.
And lastly, HAVE FUN!