In the form of classical equitation I was taught, you executed a movement by thinking of your objective instead of which aids would produce the correct result. Your mount was to appear to be the initiator, your request so minute as to be invisible and the horse's movements to flow seamlessly.
To achieve this, your knowledge of how each aid works must become as fundamentally ingrained as is how to breathe. Repetition, repetition, repetition! Your brain learns the effect each aid has, applied singly. Eventually, intuition will determine which combination will produce the desired effect and success comes without conscious thought.
Every horse is capable of picking up a rider’s minute body movements, the ones you’re unaware of making. Let me give an example: My mare Tschuess when riderless walked perfect straight lines but with me up wandered. This meant she was responding to movements I was unaware of. If I tried consciously applying aids to change her wobbly line of travel, it got wobblier. If I thought of her feet as two lateral pairs, each on one side of a straight line, it straightened. To this day, I’ve no idea how I achieved straightness, I just know that visualization was the only conscious effort I made.
These days, health issues limit me to walking. My objective is relaxation for horse and rider. Clyde, my current mount, was originally trained for the track. He lacked/lacks interest in being the fastest and became a dressage horse: Someone did a very good job of training him. He’s extra-ordinarily responsive to leg and seat aids. His trot is abysmally uncomfortable and he’s not interested in cantering. Walking suits him just fine. He has a naturally big stride and covers the ground well.
Yesterday, Clyde got damp but not out of breath in free-schooling. I knew I’d be alright on him when he put his head down to accept my bitless bridle. He was much more awake than usual: His ears were everywhere and he kept looking around. When he neighed I knew he was not keen on being out of sight of other horses. A neigh means, “I’m here, where are you?” None of the other horses answered. During all this, he still had part of his mind on me. I asked for a halt and he gave me a lovely square one.
Lately, I’ve been dreaming of dressage work in a double bridle. Yesterday, I visualized containing Clyde's hindquarters in a tight turn to left. HE CROSSED BEHIND!!! One step, a sublime step!
The theory works!