what level will you be showing at?
i suggest looking up on the USDF's website about requirements for that level.
most dressage shows will have 1-3 rings for riders to enter, you basically enter working trot, halt at X, salute, then proceed with your test. every rider who is attempting the same level as you will perform the same movements in the same order.
as far as attire for you: white (or very lite beige) breeches, white shirt, and i believe a black (don't know about navy) jacket. Some shows in the summer will let you show without your coat. Also will need a black velvet hat or helmet. you'll also need dress boots (not sure if you can use field boots in dressage...hmmm)
as for the horse: dressage saddle and pad, bridle with a USDF accepted bit (most thick o-ring snaffles are ok, check the website).
The horse should be braided with 11-16 larger braids going down the neck; the tail picked/brushed and clean, docked about 4 inches above the fetlock.
be prepared, though, it is my experience that dressage shows are some of the most expensive ones (even locally). A 2 day show at a saddlebred show (show in 6 classes) is around $250. The same dressage show (only with 2 classes) is around $500 (at least in our area :)