Most of what you need to do can be practiced at normal safe speeds. You just do it faster when driving quickly. If you can shift smoothly at normal speeds, just do that but a little faster. With most things driving related, smooth is fast. "Slamming" gears fast and furious style isn't a good way to go. Watch some track in-car videos posted on here by CSG instead of crappy movies.
I highly suggest going to an auto-x and asking for an instructor. It's cheap and low risk as opposed to a track day (which it doesn't sound like you're quite ready for). Check your local forum. Keep the ego at home and listen to your instructor. Don't try to "win." Just go learn.
- Andy