Lead changes are one of the last things I teach a horse. If you get full control over the horses hips and body the lead change will just come.
I totally agree with this. After I have done many, many, MANY small circles at a lope (both leads, counter-cantering, too) where a horse is moving smoothly and consistently I start working on lead changes. Remember that the horse must be in pretty good condition to be able to do it. My guy recently had a year off and it took us about two months to get back to lead changes. He knew how, but to do it smoothly it took a while to get back into shape.
If I were you, I would start with just getting the horse supple and responsive. Start by asking her to move forward, but at a diagonal - away from your leg. I try not to use any direct reining, just neck reining. But remember to keep your horses' body straight. Practice this at all gaits until you have the horse moving it's entire body away from your leg. Then, start asking for a more side-ways movement at a walk, little by little keeping your horses' body moving all together. Make sure the shoulder isn't moving more than the hindquarters or vice versa. After a good deal of practicing, your horse should be able to move well in a straight line (I sidepass over a pole for my reference) while keeping his body straight and his movement consistent. This may take a while, depending on your horse's athletic ability and what the two of you are capable of at the moment.
After you have that down pat, I would move onto pivoting, and once your horse can totally rock himself back onto his haunches you can move into spins.
I don't know what you mean by jumping into a canter. If you mean cantering from a standstill, then that can be accomplished after your horse has the athletic ability to do so.
For lead changes, I typically do figure eights. I will lope counter-cantering small circles (after practicing what I wrote in paragraph number one) and then transfer into figure eights all in one lead. Be sure that your horse knows the difference between asking for each lead.
Then, I will ask for the correct lead circle, do a few circles, ask for a trot and then ask for the other lead while transitioning into a figure eight. Then we'll go on that lead for a few circles. After a few days/weeks (depending) of that, I try to get it down to one trot stride and then no strides of a trot whatsoever.
We practice a lot of figure eights with lead changes, even now. After you have those, you can ask for them traveling in straight lines or whenever.
Some people will counter-canter a circle and then ask for the correct lead to try to transition into lead changes. I do what works for me.