From what I know the horse has three natural gaits -- walk, trot and canter. I base this assumption on the fact that MOST horses will perform those three gaits naturally while in the field with their friends. In Golly's case he would tell you "woah" is a gait too since its his favorite but I digress.
In the first couple years I had Golly I never saw him canter in the field. His pasture mates could be galloping across the field and there Golly would be.... trotting as fast as he could behind them. For him, canter was not a natural gait. So its something we have put a lot of effort into and because of this I've put a lot of thought into it as well. We have a long ways to go before we have a "good" canter but so far here are some things we've learned.
Check Your Horse out Medically First
When we first started to attempt the canter we got explosive bucks during the transition. I just thought he was being a pain and kept at it. Eventually he developed some light lameness. I gave him some time off but it did not improve. After a vet evaluation we decided to inject his hocks and that was the magic trick. At first he still bucked some in the transition but they gradually decreased. I think at first he was just anticipating the pain and once he knew it was no longer there, he started to accept the canter more.
If your horse is acting outside his normal character, it may be a medical issue and not a character issue.
Value of Lunging
Don't underestimate the value of lunging for a horse having trouble picking up the canter. Both "regular" lunging and free lunging (lunging at liberty in a smaller ring without a lunge line) allow the horse to find his own balance without having to worry about a rider's balance and weight. Frequent transitions while lunging is very beneficial as the transitions are usually where they are having the most issue. Mix it up though -- do quick transitions and then let him travel a circle or two without a transition.
Tips & Tricks
For every person you ask you will get a different answer on how to do a canter depart. Beyond the "how to" which I will leave either for another post (once I completely figure it out) or to others, here are some things that have helped me.
Preparation: For a horse like Golly that is more on the lazy side, I found that preparing his mind and body in the trot is important. I spend a decent amount of time making sure the trot depart is with the lightest aid possible. I don't want to be kicking him into a the trot depart but rather "allowing" it to happen by opening my hips and thinking trot. My instructor describes it as a "puff of air" pushing him forward. I imagine a sail filling with air and pushing a light sailboat down a river.
Once the trot departs are working well, the canter depart works the same way. Think a bigger puff of air and again... allow the canter to happen via opening your hips rather than kicking him into it.
Think the side pass: Another thing that has helped is that right before the canter depart I think a side pass to the outside rail. I don't actually do a side pass but I do bend Golly slightly to the inside and get the feeling of a side pass before I ask for the canter. Its a split second type of feeling. Kind of like a half halt would be... it preps him for the canter but is not actually part of the aid for it.
I hope some of what we learned helps you. I'd love to hear some of your tips for cantering in the comments section and see if we can apply them to our training.