Summarize:

Because shows are often stressful areas for horses (with all the other horses and people present), it is important to try to keep as normal of a feed schedule as possible. Get all their regular food and at least two buckets for water. When you get to the show, try to feed them at the same times as you normally would at home. The worse thing is showing up to a show missing some of the necessary tack and equipment that you will need. Make a checklist of everything you will need for the show, including any riding or exercise gear and blankets. Put all of these together and check them off your list prior to leaving, just to make sure you've gotten everything you could possibly need. Clean and polish all tack before heading to the show for the best presentation. Check with your show circuit's regulations; some bits, aids and pieces of tack are prohibited. For example, 4-H has severe restrictions on the types of bits used, and some riding clubs or associations don't allow figure-eights, draw reins, etc. Driving long distances in a trailer can be especially stressful for some horses. Rather than arriving at your show with a frightened, anxious horse, help to minimize their anxiety by bringing another horse along for the ride. They'll be much more calm upon arrival than if you hadn't. Call the event venue that you are showing at, and see if you need to bring your own bedding for the stall. Many shows require that you bring your own shavings to fill the stall with, as well as any hooks or chains, and a wheelbarrow/bucket and pick for cleaning. See what will be available for communal use at the show and what you need to bring from home - and make sure what you're bringing meets any guidelines the venue may have. No matter where you travel, it is always important to have a first aid kit prepared for your horse. Bring all basic supplies to treat for basic cuts and abrasions as well as bruises or swelling. Be sure to do the same with a human first aid kit, should you encounter an accident of some sort. You'll be away from home, so it's best to prepare for everything and anything. Pack a spare set of show clothes in case something happens to your own, making them unusable for the show. Additionally, you could choose to pack a pair of more comfortable clothes/shoes for the ride to and from the venue.
Prepare your horse's food and water. Gather all your tack. Get a trailer companion prepared, if necessary. Prepare the necessary stall equipment. Get a first aid kit prepared, for both horses and humans. Bring a change of clothes.