Make sure you have hay and water for the horse (most showgrounds have water hydrants but be sure to bring a bucket) I would suggest bringing extra tack like Brenna said, and basically bring more than what you need. Its nice to have a friend or two to help prepare your horse too :)
Here are a few things to keep in mind:
Make lists, for everything - tack, clothes, food, horses food, extra tack etc.
Be sure to bring extra tack with you. That means extra stirrup leathers, reins, girths, saddle pads, cheek pieces. You never want to be at a show and have something break and not have anything to replace it with or have to buy a really overpriced one on the spot.
You should also keep in mind that you may not be able to get as good a warm up as usual, due to cramped arenas and being pressed for time.
Follow warm up ring etiquette. Know to come to the inside of the track if you're walking, call out downward transitions, circles, and jumps, pass left to left (if you're in a country that drives in the right side of the road).
Don't be surprised or feel overwhelmed if you've been waiting for hours and then suddenly are told you have to be showing in less than half an hour. This is completely normal for shows. You have time. Don't panic.
Make sure you have someone there who you put in charge of telling you to eat/drink. It's very easy to forget, and you don't want to be riding and not hydrating/keeping your blood sugar up.
Have water available to the horse whenever you aren't actually riding. Show environments can be stressful to the horses, causing them to become dehydrated.