Yes, as has been mentioned, be prepared to fail and sometimes something unforeseen will make it go pretty badly (broken halter, etc.), but these things happen and just learn from it is the best policy.
One thing that bugs me to no end is the handler that may have a trainer or coach outside the ring giving LOUD instructions on what to do. It's very distracting and to me, somewhat unfair because if they aren't ready to go in the ring w/that horse, then they likely don't need to be in there w/out a coach in the first place. I don't mind quiet, visual cues, but the loud "stretch him, back him up" etc. gets really annoying. It's not anything other than the distraction that gets bothersome. This should be kept to a minimum, IMHO.
Respect others' space as has been mentioned, thank your presenter, congratulate your winners where possible/appropriate and of course the disrespectful things are really low class (such as throwing ribbons down and I've seen this, too, sadly).
The equipment issue is another one that can get out of hand by that I mean the inexpensive bead type halters I see breaking again and again. I know it's hard to afford certain types of show halters, but some of these show halters are really inappropriate for a young horse, a stallion, or any horse, really, that needs to be kept under control. I had one myself for my stallion and it broke and I was very lucky to catch him, but I learned a lesson I see others making and I am glad so far I have not seen anything too tragic as a result.
The best type are the betathane covered cable and/or leather and are made to stand up to a 200 lb. + horse running to the end and yanking on it. The ones w/the little thread w/the beads on it that run over the nose and attach w/a small clamp over the ring are not appropriate for most situations like showing or where firm control may be necessary, but fine for cosmetic like fun pictures, etc. If in doubt, have someone look it over for you and maybe borrow one, I know I'm usually willing to loan out a halter if someone needs one in a pinch.
Definitely do your best to be at your classes on time, but also be respectful of your horse. DON'T make him walk around and up and down for two hours or even an hour before the class as they get burned out and bored/tired/frustrated. Keep an ear on the schedule/announcer and look at the numbers in the classes previous (most managers will print out or post a printout w/the number of horses in each class) and figure out your timing for the best result. Good stewards will do first call (usually gives you about 15 minutes), second call (ten minutes or less) and third and final call (get up there asap), the other class is leaving the ring.
Ask questions and if you don't understand, ask again, so many of us are willing to help and keep things low stress as possible.
Liz