Good for you for getting a trainer! I see way too many people on this forum posting questions about teaching themselves how to jump. It's flat out dangerous. However, just to be sure, I must ask - Is your horse trained english? If not, I'd suggest you do not learn to jump on that horse. It is best to learn on a well-trained english horse. Green horse and green rider do not mix, so if your horse does not already know the ropes it is unsafe to try to teach her to jump while you are still learning. You cannot teach what you do not know.
Also, it confuses me that you are thinking about jumping if you have only ever ridden western. To learn to jump, you must first learn the basics of english. If you have only ever done western and trail riding than you'll probably need to start right from the beginning and work your way up. Don't think that you'll start jumping as soon as you get a trainer. You may learn a little faster because you have experience riding in a different discipline, but it will still take time and work.
My advice is simply to get a trainer right off the bat. There is nothing you need to do in preparation; you're there to learn from a trainer, not impress them with perfect equitation. Also when starting a new discipline, it's best to have someone experienced there to help you.
If your horse were english and you were experienced in the discipline, to answer your question lead changes are best done over the jumps. So if there is a jump across the diagonal of the arena, the horse would approach on one lead, go over the jump, and land immediately on the other lead. This can be asked for by moving back the outside leg of the lead you are trying for and tweaking the inside rein as your horse goes over the jump. It may also require some training on your horse's part. If you don't get the correct lead, you should change it as soon as possible with a simple transition or a flying. Flying lead changes are better for showing.
-----In riding horses, we borrow freedom-----