Part of learning comes from experimenting on the horse. I congradulate you for wanting to learn more.
Flying changes are fun to do, especially when you start multiple changes in a row.
Some horses will offer changes at every opportunity they get, others are more timid of the changes and may take 6 months +++ before they are confident enough to do the change.
However to rush through them can cause confusion for both you and the horse. The last thing you want is to spoil the horse.
You as a rider need to know why you are asking for the change of lead, and what you want out of it. Where as the laterals are used to improve engagement and flexion of the hocks, flying changes are a test of co-ordination, response, suppleness, ballance. (and the bonus- it looks awsome, and soo much fun to ride when trained sucessfully)
There are some things you will want him to beable to do first... a trot to canter on what ever lead you ask for no matter where on the arena. canter - walk - canter... with energy and grace & without resistance. introduce counter canter... shallow loops. Being able to sucessfully ride half halts at canter without breaking or loosing rhythm.
As a rider, you need to beable to establish clear aids to the horse. Off the horse practice riding a canter figure of 8. at the point of change, think about where your hips are, where the ballance is, your shoulders-arms-hand, new inside/ouside leg, keep tall - don't lean in. Don't try on the horse untill you are comfortable off the horse with the aids. You can also try on a 44 gallon drum (pretend it is the horse) practicing your aids. IT is best with the help on the instructor so she/he can explain it better.
On the lunge at walk without stirrups (with the help of your instructor), practice the riding aids for flying change. (if you need to) Ask your instructor to be very clear on what aids you are to use so there is no confusion.
It is far better to learn on a schooly who has done them before. I really recommend riding a schooly first with the help of your instructor.
The best way to teach a horse is over a pole or small cavalletti riding a figure of 8. This is because it encourages the horse to lift his legs cleanly to change as he is suspended in the air.
Are you planning to do jumping, or hacking or dressage?
-bec-