Skyseternalangel: Thanks :)
Raven13: I want to know more about positioning of the trot, canter, and jumping. :)
Positioning at the trot and canter is pretty much the same as what I suggested for you. Although, depending on what riding style or what in particular you are trying to achieve you may lean forward slightly in the canter and use a half seat. Generally, you only do so if you are really trying to get the horse to move forward more or if you're riding a young or inexperienced horse that you don't want to be putting you're full weight on their back yet in a sitting position because their muscles aren't fully developed and prepared to carry your weight. So that's the "depending on what you're trying to achieve" part of it but it can also be what style of riding you're doing. Like when I first started riding, I took hunter/jumper lessons and it was always "get in a half seat down the long sides!" every single time I cantered. So I would stand slightly in the stirrups and lean forward slightly. But now that I'm taking lessons from a dressage/eventing instructor she prefers that I sit the canter and sit up tall and straight. I suggest that you just listen to what you're instructor tells you to do, since they see you ride, know their horses and what you are ready for/capable of.
When you trot: If it's sitting trot, the best advice I can give you is to relax. Kind of think of your butt and thighs melting into the saddle, or even better forget about the saddle altogether..try to melt into the horse. If your seat muscles (butt and thighs) are tense then you're going to bounce, if you think about relaxing you will move with the horse and at the very least bounce less. Don't get discouraged, sitting trot is hard for a lot of people and it takes a lot of energy from your core muscles, so you may not be able to do it very long at first. It also depends on how the horse moves, if they have a short choppy stride or a big, powerful springy stride you're going to have a harder time sitting the trot than if, say the horse has a smooth gliding stride.
When you're posting the trot just feel the rhythm, count it out loud 1,2 1,2 1,2 1,2. Do you play any instrument? Posting trot is kind of like music....think of a four beat score with a quarter note, quarter rest, quarter note, quarter rest, that just repeats like that over and over again. That's posting trot. First note is the rise, then you rest for a split second, then you sit, and remain in the saddle for another split second and repeat, over and over again for as long as you want to post the trot. It's all about finding the horse's rhythm and going with it. Once you get really good at it, you can start to dictate a rhythm to the horse by posting slightly slower or faster than the horse's natural rhythm and they will adjust to you! It's really cool! You are supposed to "rise and fall with the leg on the wall", oh how that phrase haunts me lol My first instructor used to use it all the time...but for whatever reason to this day (after 12 year of riding) I still can't get a hang of that. The general idea is that while the outside front leg (if you're going left its the right and vice versa) is extending forward you should be on your way to the peak of your rise, and as it's coming back underneath the horse you should be going back to the saddle. That's called posting on the diagonal, not to be confused with changing direction on the diagonal lol When trotting a horse's legs move in diagonal pairs (right fore with left hind and left fore with right hind) hence posting on the diagonal.
For jumping: Keep the general leg position with your heels down, but you're going to lean forward when you feel your horse pushing off the ground. Let the horse close the angle of your hip for you, don't anticipate and go into two-point too soon (the leaning forward position), if you do its called jumping ahead and some pretty bad things can happen when you do that. It can cause you to get left behind and hit the horse in the mouth with a tight rein, you might get hit in the butt with the back of the saddle which is going to knock you even more off balance which could make you fall off or both of those may upset your horse and make them throw you off! If there is more than one jump close together and you manage to stay on you will be unprepared for the next jump which may make jumping it dangerous. You also want to give the horse a release with the reins, this is very important! A horse uses it's head and neck a lot for balance when jumping and in order to do that they bring their knees up and drop their head towards their knees. If you keep your hands in the same positions as when you are just walk, trot and cantering the horse won't be able to drop it's head and neck and will even be limited on how much they can bring their knees up. So in order to give the horse the room it needs to jump, but still be in control when you land you give the horse what is called a "release". There's two types: crest release and automatic release. An automatic release is advanced and you will likely not be using it for a while. You'll use the crest release, where when you jump and go into your two-point, you'll also slide your hands about half way up the horse's crest (on both sides of where the mane comes out of the horse's neck). Think of your body like a slinky. When the horse pushes off for a jump, let that push move through your body, push your butt out of the saddle, force your upper body forward which in turn slides your hands up the sides of the crest.
I hope that helps answer some of what you're looking for and maybe even give you more to think about and practice. If I had to say one thing on holding your position though I would say: When you hold yourself like how I say in my first post, if someone was watching you ride from the side, they should be able to draw a line through your ear-shoulder-hip and heel. Always think to yourself, "if the horse magically disappeared from under me...would I land on my feet?" If the answer is yes then your balanced. If not then something needs to change in the way you are positioned because you are not balanced.
And balance is the basis of all riding. If you are not balanced you are going to have a very hard time being effective with your riding.
Alright, I'm gunna shut up now! Hope I helped! Have fun riding!!