A half halt is a way to slow your horse down without pulling on both reins. It is generally used with your outside rein because your inside rein is used as a balancing aid while in a turn.
So all you do is use a gentle tug on the rein. The movement of your hand depends on the amount of pressure you already have in your horses mouth, along with the length of your reins. For example if your rein is longer and you have a very light feel in your horses mouth, then generally you will have to move your entire hand, elbow, and shoulder together slightly back. Just slightly, and after you feel the increase of pressure in your hand, you release. If you keep your rein shorter and have a steady and constant pressure on your horse's mouth then all you really need to do is close your fingers even tighter or close just your ring finger even tighter until you feel the slight increase in pressure and then release it again.
The general rule that I follow when using a half halt at the posting trot is to half halt with my outside rein whenever I sit. This way my leg is a little bit stronger to keep my horse trotting, but my seat is a reinforcement to the half halt.
At the canter, the goal is to use the half halt every time the horse's mane raises up. If you just glance down you will see the end of your horse's mane flip up once through every stride that they complete. The reason you want to half halt at this point where the mane raises is because at the second, both of their front feet are off the ground so the half halt is much more effective to slow them down and correct their balance.
Hope this helps.
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