Everyone has their own way and I simply took the fact that horses learn patterns very quickly and turned it into my advantage. If the horse has good balance in the canter and counter canter (which is a prerequisite for doing FC in my opinion) then the following should produce clean balanced STRAIGHT FC in a short time.
I have posted this befor so will just copy it.
Here is how I got them. Never late behind, never got cross canter but good clean changes.
You must assume that at the point of trying this I had a comfirmed canter on both leads and could do counter canter at a reasonable degree of collection. In other words not perfect CC but certainly good enough to hold it around corners.
I never try to get flying changes from the trot to canter or canter to canter. The possibility of cross-canter, rushing and an unbalanced canter is too likely to happen.
My preference is walk to canter or halt to canter and I think you will find that a disunited canter is EXTREMELY rare under these circumstances.
I also keep in the back of my mind that horse are notorious for learning something in certains areas of the arena and once done in a certain place and way will repeat that pattern over and over again.
That being said I simply teach the horse a pattern.
I will canter a few strides then walk,then counter canter a few strides then walk. I will repeat this exercise for as long as it takes. I usually start on a circle and the amount of canter strides is unimportant in the beginning. If the horse gets excited (some do) then go on with something else and try again later in the ride or another day.
When the horse accepts the back forth pattern on the circle go anywhere in the arena and I find the straight side is very good. In some cases the horse may respond better on the straight side first before the circle and that is also OK.
Slowly shorten the number of canter strides between each change of lead. If you can "feel" your horse you will almost "know" that the horse is ready for the first change from the counter-canter to the regular canter and if it is done on a curve (corner) you have a very good chanch of getting a clean change (front and back). Go back to your "pattern" and wait for the next "opportunity". I prefer at this time to try to go to the halt canter to halt--then counter-canter halt---canter halt--etc, Again when the opportunity offers itself the flying change from the counter canter. It is impotrant to ensure that the horse is walking or halted and not rushed back to the opposite lead too soon. The length of time between each canters are shortened as you go along and the possibility of 2 changes could be possible.
I am sure that you understand that you will need to switch direction from left to right rein so that your counter-canter opportunities will able to be exercised on both leads.