Hey there, welcome to Newrider.
First off, the aids for canter.
Sit deep in the saddle. Keep your inside leg on the girth, and slide your outside leg back, so you 'sweep' it from it's normal position, about 6inches. Squeeze the horse and it should
pop into canter. 90% of riding horse wont though!
why doesnt the horse just start on the correct leg anyway?
It's all to do with balance - if you are not sitting completely square the horse will have more weight to one side and will push off on the wrong leg. Some horses do it anyway, because horses - like people - are often right or left side dominant. That's why horses are nearly always harder to ride on one rein than the other.
If the horse is on the correct 'leg' it will seem to be taking a longer stride with it's inside front leg. It will also be bent slightly to the inside. If it's on the wrong leg, the outside front leg will be taking the longest stride. If that happens, come back to trot and try again, trying to sit with equal weight on each side.
But does this mean that i kick as well or what?
Dont kick at all - it doesnt work. Imagine instead that you are trying to squeeze the horse like an orange between your calves. If you kick you will fall forwards and take your weight on your knees, which will be harder for you to get a canter from. Also horses dont really respond well to kicks as it makes them 'tune out' and ignore you. Squeezing works better, and looks nicer too
I also can't get the idea of my bottom "sweeping the saddle"
Im not entirely sure what she means there... I think she may be suggesting you move with the horse, in a 1-2-3 tango type movement. Just try and sit lightly, and really push your bottom underneath you so you feel like you are sitting right on your seatbones. You'll find it easier to sit up and get a good position if you do that. Really feel like you are opening your hips and dropping your legs down, and letting the horse carry you along lightly.
Sitting deep in the saddle will come to you! Dont pull too hard and try not to sit heavily - imagine someone holding the top of your hat and pulling - your whole body should drop straight down underneath it. Your shoulders under your ears, then a straight line through your hips and into your heels. The best way to sit deep is to really relax your leg and sit back - this will also take the weight off the horses shoulders and make the canter transition easier. Try and keep your knees open off the saddle, and drop your weight into your heels (without sticking your legs forward!
Hope this helps, and enjoy Newrider!
Go introduce yourself in the Cafe Area and Im sure you'll get lots of people to chat to soon