All I can say is "Practice, practice, practice!" I'm tuning up my appy to start showing him again, and for showmanship, any time I lead him, I ask him to set up at least once or twice. Getting your horse to set up quickly will be a big advantage. The pivots and backs are also important, as PBritton pointed out. Other points to consider (depending on your level of experience):
1. Straight lines. It really helps if you make sure you lead your horse exactly where you want him to go.
2. Patterns. When presented with a showmanship pattern, pay attention to which side of the cones you're supposed to be on. If you have to pivot at a cone, make sure you leave enough room that you don't step on one or knock it over. If a pattern specifies a number of steps to back, make sure you do that, too.
3. Pivots. When a pattern calls for a pivot, make sure you finish it. By that, I mean, if you're supposed to do a 180, make sure you pivot the full 180, not 175 and then walk into line.
4. Backs. Back that horse up straight.
5. Stops. Make your horse stop straight, and not too close to the judge. AT LEAST an arm's length away.
6. Quartering. I especially practice this when I'm training a new horse for showmanship, because I've had some that like to move when you do. It's important for him to be able to stand still and attentive while you move around him.
7. Grooming. He should be clean and shiny. His head should be clipped, as well as his legs. His feet should be the proper length and well balance, and they should be polished. Tails should be clean and "fluffed", you know, no tangles or strings. Short manes should be banded. If, for some reason, you wish to keep the mane long, make sure it is clean and well brushed, but for any of the regional shows or higher, it's a good idea to shorten and band it.
8. Your Attire. It should be clean and fit well, regardless of what you wear. Boots, buckles, and belts should be polished. Hats should be cleaned and shaped at the beginning of the show season and as needed throughout.
9. You. Your posture should be erect, your movements crisp (but not jerky). You should always know where the judge is, and look like you're having fun.
These are mostly things I've learned through doing it wrong, at least once. I'm sure I could write a lot more on this subject, but I think I'll let your eyes have a rest, LOL.