I use a placing pole on the center line and work on a figure 8 over the pole. I first do simple changes, over and over and over again (obviously not consecutively) at the trot and then also the walk and halt. Some I halt before the pole, some just after, some I try and halt over, etc and same with my canter-trot and canter-walk transitions. With the last mare I taught, first time I asked for a change over the pole (using this same method), she got it immediately. I continued the same process for about a week with always starting on the simple changes, and then I'd ask for one change at the end, give her a big big pat and call it a day. After that, she had them down to a pat and she'd do them wherever I asked. She was very intelligent, though, and picked everything up usually after one or two goes so it was no surprise she had the cue mastered after a week.
There have been a few of these threads. I won't go too too much into detail since you can search for them if you want more but....
I don't use the center pole as I find it can teach a horse to change late behind.
I establish SOLID correct leads and I encourage you to work on lots of the tougher transitions including walk-canter, canter-walk, halt-canter.
I will only start teaching changes after my horse is loose, 'up' and very responsive. If the day didn't go well, save it for another day. Changes can be stressful.
I never teach changes on the diagonal. ALWAYS a figure 8. I have taught on the diagonal and it gives me trouble when riding a diagonal line o/f's and my horses swapped, mid way.
Always teach the horse to change when a new bend is established and not before. This way if they learn auto changes you can control the change if you don't want it.
Overall, I pick up canter to the direction the horse prefers the least. That way when I ask for a change they WANT to get on that other lead.
I start my figure 8- hold canter- straighten- passing middle change bend and ask for the correct lead- holding canter. (Keep your balance).
I do this to give the horse the idea that I am asking for something and to see if they can get it.
If they don't get it, trot, canter immediatley.
Repeat 2-3 times the SAME direction.
Call it a day as long as they kept their cool during the lesson. Otherwise, work on a few simple things he/she does well and call it quits and don't try teaching it again for atleast 3 days.
(I say 3 days due to the way a horse's mind 'learns'. Google it, very interesting really and so true.)