Essentially, all you have to do is sit and feel what the
horse is doing. Then you compare the input you get via your seat, legs and hands to your knowledge of what it should feel like. The discrepancy between the status quo and the ideal will tell you exactly what you need to do. After studying all the theory, this is what riding comes down to. Sit, feel, observe, compare, adjust. The difficulty lies in looking at the horse's gait with a powerful enough microscope, so that nothing escapes your notice. The other difficulty is to observe every single step, and to respond immediately, within the same stride, when the gait goes off course.
To stay with your example of bending the horse on a circle: If you feel that the
outside hind leg is falling out, bring your outside hip and the entire leg more back, and drive the hind legs
towards the inside shoulder. If the haunches swing to the inside, bring your inside leg back, and perhaps rotate your pelvis, so that your outside hip comes more forward. If the horse is stiff and does not want to bend, maybe you have to increase the spiral seat.
If the outside shoulder falls out, catch it with your outside knee and rein. If the
shoulder falls into the turn, catch it with your inside knee and rein (acting against the base of the neck, rather than the mouth).
One thing that is especially
important with respect to bending, that I have not found in any book, either modern or old, is that your seat is adjustable in three dimensions. Take advantage of that. Experiment with that. If your horse is resistant, and you keep adjusting your seat in all three dimensions, you will sooner or later end up with an alignment in which all the tension leaves the horse's body, because you have harmonized yourself, your own body alignment, with your horse's. That is something that is very difficult to teach, because it is so individual and often so subtle, but it is the most powerful adjustment you can make.
Since we are all built differently, you cannot transfer the precise alignment from one rider to the next.
You can only teach concepts and tell the student to play with them, until they figure out for themselves what works. The teacher can make suggestions concerning the alignment, and he can give feedback, but the horse's feedback is actually much greater, clearer and more impressive than anything the teacher can say.
To give you a brief example, you
can adjust your hips three different ways. You can bring one hip more forward and the other one back, or vice versa. That's one dimension. You can tilt your pelvis forward or back. That's the second dimension. You can lower or raise one seat bone. That's the third dimension. The correct alignment will involve a combination of all three dimensions. The same thing applies to the shoulders. However, in my own experience, the hips are more important. Any adjustment should begin there, while the shoulders are then co-ordinated with the hips in a second step. Dr Thomas Ritter