I was always told that the basic drill to teach lead changes was to start by working in a figure 8 pattern. Start with the jog (or trot) and when you get to the center of the 8 ask for a right lead canter. Canter a right hand circle and come back to the center of the 8. Break to jog for a couple of strides and ask for left lead canter. Repeat.
Eventually there will be less and less stride necessary to pick up the other lead.
Keep in mind, your transitions will need to be almost perfect for this. If you cannot pick up a canter from a trot nearly immediately, you will need to perfect that before trying to get a flying lead change. Also, be sure your horse is very sensitive to your cues. You shouldnt have to trot your horse into a canter. When you ask, they should pick it up immediately, from a walk as well.