Issywizz suggested I sticky this reply to one of our members, which was posted by me on the Society forum. Sarah felt that it gave a neat precis of the aids and was worth preserving! So here it is for anyone that is interested.
I never, ever lean back to stop a horse. If you do this, you are depressing the very area of the back that we want to lift into the halt.
The seat aid I was taught by my German trained trainer as I explained in the book, Enlightened Equitation, is a closing of the seat muscles. This can be varied from a quick, sharp closing, as in a canter halt transition, or slightly less, for instance, canter to walk, and less still for canter to trot. It works on every horse, instantly, provided the rider is sitting correctly in the ear, shoulder/hip/heel line. It lightens the seat by lifting the skeleton, but leaves the buttocks in contact with the saddle. I demonstrate wherever I am doing a lecture demo, on a horse I have never seen before, not even a few mins before the demo, and it never fails. It is invisible to the onlooker, but totally clear to the horse.
I never, ever teach use of the heels for forwards movement, nor do I use this myself. I teach the inner calf, activated by a lowering of the little toe, to close, or release, so that again the aid is invisible, never backwards, always slightly inwards with a little roll of the calf muscle. When released, the leg should not ping off.
In an upwards transition, I would also not give the reins, this causes the horse to run into the next pace, instead of stepping up into it. I do not want my contact to change, if the horse is correctly on the bit, and accepting a light feel - someone once likened it to shaking hands with a little old lady, you neither want to pull her over, nor push her over!! But it is an excellent description!
My legs would be used first in an upwards transition, never the seat to push. I can turn my hot Lusos into a riding school plug in a split second, by pushing with the seat, was only demonstrating this to a student yesterday on Sudi.
In a downwards transition, the seat muscles closed, with a light closing of the lower leg to keep the hindlegs coming under, and at most, a squeeze with the fingers, or vibration of the reins, on a really educated horse, not even that. The seat aid should be sufficient to effect a downwards transition when the horse is well schooled. My old mentor, Capt Desi Lorent fined us a drink down the pub if he caught you even slightly pulling back on the reins, and at British pub prices, you soon learnt not to keep him inebriated!!