The biggest tip I can give is to open yourself up to the horse... I don't know if that really makes sense. If you have a trouble-maker of a horse, don't get frustrated.. but make the adjustments, keep a level head, and ride on. Jumping is complicated; there's a lot to keep in mind, but as long as you stay still (on the inside. and thus move with the horse) it should be a lot easier. I dunno... jumping for me is kind of therapeutic so I'm just naturally calm and it helps me to keep balanced and riding well.
Second, always always always keep in mind that your heels should be down. If your heels are down, you will automatically be gripping lightly with your legs and it should help to keep your legs still. You might be jumping for the horse, too. If so... count the 3-4 strides before the jump and it'll help establish a rhythm so you're not jumping ahead.