Disclaimer: I haven't showed in a while, but I've been keeping up with trends and whatnot. I'm sure there's some things I'm leaving out, but this should be a good start for y'all. Basics:
-- Firm, quiet legs that don't bounce all over the place. Calf on horse, just behind girth.
-- Heels down
-- Hands quiet, fingers together, just above and in front of the withers
-- Correct diagonal & lead
-- Keeping horse going at an even pace
-- Good posture, shoulders back, head up and eyes ahead
The best thing you can do is just have someone watch you ride so they can point out the things you're not aware you're doing. Bouncy hands, loose leg, etc. Also, try and watch a few shows so you'll know what class to enter and how everyone else looks in comparison. You could also look up some videos on YouTube of equitation on the flat and see how a class is done.
Here's the USEF document that lists more exact details: http://www.usef.org/documents/ruleBook/2011/12-EQ.pdf
You'll see the Hunter Equitation stuff in the first section. It also does a brief description of rider appearance and bits/bridles/reins that are not allowed. You just have to scroll a bit.
Also, what the judge can ask of you is listed under EQ113 of that PDF. That's for everyone though -- from novice to open, IIRC. So, if you're in a novice class, I seriously doubt they're going to be asking you for a hand gallop or a figure 8 with flying lead changes.
I've never done the upper classes, but when I was showing it was ... Walk - rising trot -- sitting trot -- sitting trot with no stirrups, then picking up your stirrups without moving around much -- change of direction -- halt -- canter -- simple lead changes ...
It would also help if you called the show organizer or your trainer and asked them what would be asked of you in each class. As for appearance:
A lot of this depends on what kind of show it is. It would probably be best to ask your instructor, or view photos from shows in the area. A/AA shows are more strict, while local shows tend to be much more lax -- i.e., no braiding for horse, riding in non-traditional colors, etc.
-- Hair in a net, unless you have a boy cut with no tufts hanging out from beneath your helmet.
-- Green-beige or beige breeches
-- Rat catcher shirt -- can be just about any color, but white is classic
-- Navy or black coat
-- Black helmet (although I've seen other colors popping up)
-- Tall boots, field or dress. Although in some local shows, matching 1/2 chaps and paddocks will be fine. Just no brown boots with black chaps, etc.)
-- Braided mane and tail (Usually not necessary at lower level shows)
-- White fitted pad
-- Clean tack
-- Clipped whiskers/face
-- Washed, thoroughly groomed