If we all remember I posted this on the half halt thread....
Try starting off with just driving the horse on alternate sides. Go slow and don't rush. If you close your eyes you will feel the stomach of the horse go from its left side to the right so wait until each of your legs feel this and bump the stomach to the opposite side. The stronger the drive the more forward the horse, so don't over do it.
If you feel you have this down then add the rein aid for the half halt remembering that if you drive on the left side the right rein will be giving the aid. Again go slowly.
Once you have the co ordination down then the only thing you need to do is match or allow more drive or more rein aid.
If the drive exceeds the rein aid the horse will go more forward ( and lead into your extensions)
If the rein aid exceeds the drive the horse will go into support mode and lead into collection.
What you will also find if your horse does not quite have the frame you would like it should automatically come into the frame according to the balance you have achieved.
The problem with most people is they do not associate one thing taught to them with the next and that they are interwoven. You cannot throw a half halt in here and there even if it is timed correctly and then forget it until the horse goes off course.
We all know the walk and that if they feel the horse, that the stomach goes from left to right. If the rider felt this sway and sat deeper on the side the stomach swings to and pushes the stomach back they are in effect opening up the gait and getting the horse to "march" which is what the judges are looking for.
Now we all know that the trot is a diagonal gait, and taking what I quoted above would mean you will drive alternately according to the hind leg that will be in flight and depending on the strength of the rein aids will either shorten the stride or allow a longer stride.
In the canter the horse leg movement is entirely different with most people using the inside leg to drive and the outside leg to ???? The question marks are here because people disagree on what it is for but I will elaborate.
So you are walking forward and allowing your hips ( should be open and loose to feel this movement along the back as well)to swing with the alternate swing of the stomach. This aid will travel along the riders leg so it hugs each side as the stomach returns there( but does not poke or stab).
So now you want a trot but not just a "nice" trot but a forward working one. In this case the rider needs to feel which leg is in the correct position and aggressively drive where the aid will be sharper ( later in training not so much).
So without changing your position ( other than sitting deeper) your alternate drive initiates the trot. What trot you get will depend on you as the rider sending the one set of diagonal forward, feeling the lift of the horse's body and THEN applying the appropriate half halt and following the forward movement of the horse. Wiggling or playing around with the reins BEFORE the rider's leg has driven the horse forward is totally useless and is a good way to get the horse to "hang" in the bridle.
So now that you have a good forward trot ALL you have to do to get the canter is STOP the outside leg from driving and apply inside leg only. The outside leg MAY be needed to prevent the haunches from swinging out but if you have your horse forward and straight in the trot which, using the aids I posted above RARELY happens.
This is the seamless transitions that everyone looks for.