Use a combination of seat, leg, and rein aids just like you do to ask for canter in the first place. If you are going from a left lead canter to a right lead canter, slide the left (outside) leg back and squeeze, while driving with your left seat bone and using the reins to support and keep your horse straight. It's also very important to make sure your horse is moving in a collected canter. It's much easier for them to make the transition if they are using the hind end correctly and going with a nice round movement. Like the first replier said, do simple transitions first using the cues we talked about so your horse starts to get an idea what you are asking for.
The best way to practice is on a figure 8; don't make a diagonal line from corner to corner though, make a straight line from side to side at the half way point of your ring so that the direction change is more last minute. The more abrupt (but not too abrupt) change will encourage your horse to shift weight to the opposite side, and also change the lead. If this is new for your horse, start out with simple changes at the center point of the ring with as few trot strides as possible. Once your horse is getting the hang of it, then try the flying change.
And most importantly, have patience. This isn't something you and your horse will learn in one or two days. It could take months. Horse do the flying changes naturally and comfortably out in the field, it's just a matter of them learning to do it with a rider and when asked. Best wishes and happy riding to you!