Depending on what type of show it is, the craziest thing they'll ask for outside of w/t/c is a sitting trot. If you are riding in a breed show or 4-H show, equitation classes typically have a pattern that is posted ahead of time for you to memorize. It can include transitions (walk at this cone, stop at this cone, trot a circle at this cone, canter on a specific lead, figure 8, etc). They aren't anything too crazy. Do keep in mind that during flat work you will have to transition to a canter from a walk, not from a trot.
Outside of all of the good riding technique already instilled in your head, there is one important key: always know where the judge is and make sure you get seen. Always try to be one of the first horses in the ring, and enter at your best gait.This is a great way to get noticed before the class technically begins. If your horse has a great trot, enter at a trot. Be sure to come back to a walk when it looks like all the entrants are in the ring. Don't get bunched in with other horses. It's ok to cut across the ring or circle to get a spot on the rail by yourself. At the only A-rated show I competed in, I pinned in a flat class of 38 horses because I knew where the judge was and was able to get by myself and get noticed.
Practice standing still! When you line up for the results at the end, you want your horse to stand square (all four legs even) and alert. Don't give him a loose rein or let him drop his head and sit in the very best form you can must.
Make sure your boots and your horse's hooves are polished (a mom running around with a towel and hoof polish is a great thing to have as she can spruce you up right before you head into the ring). Be neat and clean, and keep it conservative for English riding. No crazy colors or sparkles.
Be confident, relaxed, and have fun!
Remember that it's not all about the ribbons. If you go out there and have a good ride, you are successful. The ultimate goal is to do the very best you can and ride to you and your horse's potential. If you are better than the other competitors, then great!