The speed of the round should not change very much from the controlled gallop. Judges don't like to see horses that get stronger and faster throughout the course.
The horse should also jump with its knees even and legs lightly tucked beneneath it. This is a good trait, because it mean the horse is less liable to drop a rail. Dropped rails usually mean that you won't place.
Good manners are also important. A hunter should be kind and obedient, and should be happy to do its job. The horse should not be bothered by the colorful flowers or decorations on a jump. The horse should not wring his tail, pin his ears or buck either.
The horse must also take each jump in stride, and not take off too far from the fence or put in a tiny stride just before (called a chip).They ruin the flow of the round.
Remember that judges like to see a horse they would like to ride. Think, "Would the judge want to ride my horse?"
They will take off points for knocked rails and bad form, such as twisting over fences or letting its legs hang down. They also take off points for wrong leads, refusals, and if you use your stick they will take points off for that, too. They also penalize if your horse carries his head too high or if you cut corners.
You get a score after your round. The horse with the highest score gets the blue ribbon, and second highest places second, etc.
If you had a really good round, you will get something between 80 and 90. If you had minor mistakes, that would be something in the 70 range. If you had major problems such as a dropped rail or you had to use your crop, you will get a low score of 50 - 60. That can be lower if your horse bucks or refuses.
I have also seen people marked down for improper attire, such as half chaps rather than tall boots. Please remember to read the rule books as well, so you don't get into trouble for improper attire or "illegal" tack, etc.
Sorry it's so long but meh xD