Well, I'll have two weeks of cantering under my belt Tuesday, so I'm an expert...not!
However, here is what I did:
I make my jumps in training by using an Australian style or western saddle until I'm comfortable. Then I try it in an English saddle. When I'm comfortable in an English jump saddle, I'm ready for the next step - in a western saddle.
I worked on sitting the trot until I could do so without thinking or effort. I figured if my sitting trot stunk, then I wasn't ready to go faster.
If possible, I'd have used a lesson horse and started on a lunge line. But I couldn't find a place for that, so Trooper - who hadn't cantered with a rider in a year - got the call.
I used an Aussie saddle with a horn. I pushed him faster until he broke into a canter. We did perhaps 3 strides, then he slowed down. Once he realized I wanted him to canter, he was eager to comply.
I had to hold the horn when he would start, and I had to neck rein him with the free hand since he wasn't very good at judging turns. And I bounced. A lot. That was because I was trying to sit the canter, which doesn't work like it does at a trot. See buffoonery below - I'm flying in formation with Trooper, not riding him:
I then realized I needed to move my hips with the motion. I stink at dancing, and it showed. However, I also was losing the stirrups. So I stuck my feet into the stirrups as far as they would go, wearing my cowboy boots with 1 5/8 inch heels. I then sometimes lost contact with the stirrup, but my foot stayed in the stirrup. With my boot and the stirrup I was using, I wasn't worried about it going THRU the stirrup.
Then Trooper and I started cantering. Anywhere from 30 sec - 2 minutes at a time. I quickly realized that holding the horn makes it harder to canter, since it hunches me over and prevents me from moving my hips as needed to ride the wave. So I would hold on for the quick start, then practice releasing it for a few strides.
After a couple of 30 minutes practice sessions (with maybe 5-8 minutes of total cantering), I started to get the feel. As of yesterday, I didn't grab the horn once. Not even going from a walk to a canter direct. It is tempting to grab the horn, but it makes riding much harder.
I need to tilt forward a little, and move so my hips are under my shoulder at the most forward position. Some people move their hips from behind then to in front, then back - but if my hips get in front of my shoulders, I lose the rhythm.
And based on my whopping two weeks - almost - of cantering, getting in rhythm with the horse seems to be the key to keeping my butt on the saddle, shining it with my butt cheeks.
Now, how not to be scared? I don't think there is a way. But you can cut your risk by using a reliable horse, and a deep saddle - western or Aussie. If you can't use a lunge line, use an arena big enough so the horse isn't stuck on the rails, but small enough that he can't go wild. If you are good at sitting the trot, your seat will be good enough that you shouldn't come out completely, even if you buffoon it the way I did my first try. But don't try to sit the canter. Polish the seat with your rump. Breath in thru your nose, hold for a 3 count, then exhale loudly thru your mouth. Try to force your knees away from the saddle - you cannot rock in motion with your horse if your knees are gouging the saddle!
Then do it. 30 seconds to a minute. Slow. Relax. Repeat. You cannot learn it without doing it.
But there is also no rush. I've been riding for 3.5 years. I'm a very slow learner, and my previous experiences with cantering was for Mia (my mare) to do it for 1-2 strides as prep for a full-bore panic bolt - so I had lots of bad memories.
All just IMHO. I am painfully aware how utterly lacking I am as a rider - but maybe that gives me some insight into how other beginners feel. And this picture from Wiki helps me get the idea of moving my hips: