Thanks for the great questions. To me, it is two distinct questions you ask, 1) how to teach canter departures, and 2) how to feel leads.

As CHA suggest, I like to teach cantering in a progression from the most simple to the complex. First I just want the student to be able to sit the canter and know what it feels like. I'll get them into the canter anyway I can and not be too concerned about what lead they take. After checking the girth again and reviewing how and where to stop, we'll urge them into a canter on the long side of the arena (trying to avoid a turn where they might get off balance). At this stage, the biggest difficulty is to get the rider to offer a release to the horse when they ask him to canter and not to pull back on the reins when the horse does canter. I really emphasize the importance of the release by showing a horse cantering and how his head drops down with every stride and if there is not a release, then the horse hits the bit when he drops his head so the rider is cueing the horse to stop.

Once the horse is cantering, I just want the rider to go a few strides at first and try to feel the rhythm of the canter and make a circle with her hips like pushing a swing. One of the common problems seen at this stage is the rider too far forward, with a closed pelvis, so instead of moving with the horse, the rider is thrust up and out of the saddle with the lift of the horse's back. I find it helps to emphasize keeping the shoulders back over the hips and when you push a swing, your hips will actually go behind your shoulders momentarily.

Once the rider is able to sit the canter well, she is ready to learn to feel the leads. It is really quite simple. If the horse is on the right lead, his two right legs are moving in front of the left legs (this requires another demonstration allowing the riders to watch a horse cantering). Now, if the horse's right front and right hind are in front of both left legs, what do you suppose you would feel in his back? When the horse is on the right lead (and visa versa for the left lead) the right side of his back is more forward so the rider will feel her right hip and right leg in front of the left. That is how you feel the lead. Caution riders that they should not allow the twist to come into the upper body, but it is okay to feel it in the seat and legs. Conveniently, this is the position your legs should be in when turning or circling, outside leg is back at the hip to give direction, the inside leg is at the girth to encourage impulsion and a bend in the horse when he turns right.

I never teach riders to look down at the lead, unless they need to verify what they feel. Once a rider becomes dependent on looking down for leads (or diagonals) they will have great difficulty learning to feel it. It takes a lot of discipline on the rider's part to try and feel first and then, if necessary look down only to verify if what they felt was correct.

For canter departures, there are a lot of skills that precede good departures. There is an old saying in horsemanship that says, "the best way to improve the canter is to improve the trot." For good departures, the rider must be able to ride the sitting trot well, ride smooth transitions between halt-walk-trot, collect and extend the trot and ask the horse to go haunches-in. The haunches determine what lead the horse will take. If the haunches are to the right, the horse will take the right lead. If the horse's haunches are to the left, he will take the left lead. Riders need to understand not only what aids to use (outside leg for canter cue) but also why that aid is used.

Another important component of canter departures is preparation of the horse. I like to use an analogy of John Lyon's: If I want to call and ask my friend to bring me a gallon of milk, I go pick up the phone, dial her number and wait for her to answer, before I can ask her. At this point, I can shout into the phone as loud as I can, but nothing will happen until she picks up the phone at the other end and says, "Hello, what do you want?" To prepare the horse to canter, we must prepare him for the cue and wait until he picks up the phone and says, "Hello, what do you want?" This is done by shortening up the reins a little and applying a little leg at the same time, to gather up the horse. When the horse's head comes up a little and his attention is on the rider, he is ready for the cue. Then the aids need to be applied: outside leg (to place the horse's haunches in), a release of the reins, a slight elevation of the inside rein, a push of the seat (the same motion of your seat that happens when you canter, you can't post a horse into a canter because posting means you want a trot), and what ever voice cue you use (I like to use a kissing sound for canter and not use it for any other cue).

Because a horse's mind works quite slowly compared to a human mind, it is useful to break the cue down into a progression that the horse can learn to recognize as a specific cue. I like to teach riders to apply the aids in a rhythm with a pre-signal, so the horse has time to think through the cue and be ready. The order in which you apply the aids might be different with different teaching styles, but what is important is that they are applied in the same order every time with a slow rhythm.

The canter is probably one of the most complicated things we teach. The more you break it down into small components, the better the student and horse will respond. These techniques are just some of the things that I have found success with, but there are many effective techniques that may vary somewhat from these ideas. What is important is that your lessons are safe and effective (and fun!) and that you have developed a progressive skill-building plan. Good luck!