1. Hunter Showmanship
This is an in-hand class. It will typically involve a short patter that will require you to walk, trot and possible pivot the horse. You will then set the horse up square (meaning all four feet are lined up) to present to the judge. As the judge walks around your horse you will have to move around the horse. It's a teeny bit hard to explain without showing you, but look up some videos on showmanship on youtube and you should be able to figure it out. You can usually show the horse in a hunt bridle or plain leather halter. Check the rules to see if it specifies.
2. Hunter Under Saddle
This is an under saddle class (obviously lol) where the horse is being judged on quality of movement, consistency and responsiveness to the rider. It's pretty straight forward you'll be asked to walk, trot and canter both ways of the arena, and asked to back up either in the line up or on the rail. 3. Hunt seat Equitation
Similar to Hunter Under Saddle but you are being judged instead of the horse. You may be asked to do a short pattern and then be judged on the rail. They will be looking at your position and how well you control the horse. You will probably be asked to ride without stirrups, so practice that. 4. Hunter Command
5. Catalog Class
I'm not familiar with these two. 6. Bareback Dollar
Someone already described this one. It's a blast and will really challenge your leg muscles 7. Trail Class
Is like a mini obstacle course for your horse. You may be asked to walk over bridges or tarps, get mail out of a mail box, open and close a gate, back through ground poles, turn around in a box, etc. etc.