I copied this out of one of my other posts.
For pivots you will first need to decide which rear foot you would like your horse to plant. Horses naturally plant their left foot to turn clockwise like you will be doing in showmanship. In the US at the Quarter horse, Paint, Pinto, Appy ect. Shows the right foot is the preferred foot to plant for turning clockwise in showmanship. Your first step will be to get your horse to move his shoulder away from you as you walk towards him. A dressage whip can be a useful tool for teaching this but do not get aggressive with the whip. Use it as a barrier between you and you horse and tap him lightly if you move towards him and he doesn't move away. After you teach them to move thier shoulder a lot of your work is done. If they are moving their shoulder properly there will not be a lot of movement out of their rear hooves. When you get the shoulder movement down start to focus on the rear legs. If you are going to have your horse plant his left foot you can kind of push their weight back onto that foot for your turn because the right foot is going to back around the left foot. If you are going to turn on the right foot you will need to slightly pull them ahead because their left foot will need to walk forward around their right foot. Start by only taking one step at a time and eventually increase the legth of your turns. This can be a very frustrating process so please take your time and be very patient with your horse. Also, if you get a chance practice your turning with a horse that already knows how to pivot, you will learn a lot.
If you need more explanation let me know.