What everyone said, to put it together. Depending on where you are in the training, from first asking for the canter to first asking for flying changes, it depends on the subtleness.
The final goal is one tempis, where you’re really doing it from lifting up the inside seatbone. But, that requires, as Mystic said, the set up of the horse off the new inside leg and responsive to the supportive outside. You see swinging legs in tempi changes because people are thinking too much from the leg.
Young horses we often get the canter whatever way we can. Ideally they have learned the verbal cue, and some speed and off the back helps. When they are new in the canter depart, we may have to be stronger and more obvious with the outside leg. As the develop, ideally you have taught them to give to the inside leg and rein, have a supportive outside leg to set up, and are teaching them a left/move of the inside hip gets the canter. Think of their legs–they need to step under with the new inside and lighten off the new inside to get it.
You have to also deal with the individual horse and what they need. Right now I just started my 6 year old on changes two weeks ago. Some horses after teaching them walk canter walk help get the idea thinking more with a touch of the inside whip. With her this didn’t work at all. I need a strong outside leg to cue the change AFTER I’ve got her supple off the new inside rein. She does them very, very well–one of the easiest horses I’ve ever trained. Down the road when she’s solid here, we’ll work more on just supportive outside leg and more/only inside hip.
We always get crooked and tweaked if someone isn’t watching us. I need to be reminded more from the hip and not to lean over. The George Morris article really stuck with me, too, and I always keep that in mind–sit, straight, hands up, and forward.