If you have time, a full body shampoo the day before.
Use a soft rubber currycomb to work the shampoo into the fur, to remove all excess scruff and dirt.
Rinse well, again rub over gently with a currycomb to get the last loose fur out. (Pay attention to any lighter fur or white spots, as those showcase dirt blatantly)
If you have it, then use a special mane/tail shampoo.
While wet, comb with your fingers first, then with a wide-toothed comb, the mane and tail. Be gentle. No one likes to have their hair yanked on. Start from the bottom and work up.
Apply a generous amount of conditioner to the tail, but only to the ends of the mane. (If you're NOT going to band the mane, then you can put a little conditioner throughout)
Squeegie off excess water, and allow the horse to air dry. Pray that he/she doesn't roll around in the stall. XD
Well before the show, brush first with a very stiff-bristled brush, over his/her entire body, and a gentler bristled brush for his/her face. (Again, who wants a hard brush to the eyeball? Ouch)
Just before the show, you can take a cloth that is DAMP not dripping, with a mix of water and rubbing alcohol, and rub your horse down, to remove the fine dust that will have gathered while you guys were walking around. Avoid the face, though, because the fumes will not please your horse.
Make sure all riding equipment is polished and shining.
If you want, you can add a little whitening agent to any white spots on the fur (Chalk or baby powder works)
Don't go overboard, or sweat will make it run into darker fur.
You could also use hoof polish, if your horse has dark hooves (black polish on light hooves doesn't look good. haha) Clear Polish works well for other colors. make SURE you do this when your horse won't be stomping around in dust or straw or sawdust for a good 5 minutes. Otherwise you'll ruin the shine with gunk that will get stuck in the drying polish.
Do your best, and SMILE!
Have fun!