GREAT advice so far. Yup, did three Reg Pridmore track days in the early 2000s, and that has saved my bacon countless times. Do a good track day with good instructors. Look where you want to go, not at the danger (target fixation, as mentioned before). Relax your grip, and grip with your knees. BREATHE (you would be surprised...). Lean farther; modern motorcycle tires have amazing grip. You have run out of clearance when the solidly-mounted parts start scraping, not the spring-loaded peg feelers. Pay attention to the force you are putting into your (relaxed) grip on the bars, and consciously countersteer; it really does work. Even if you don't slide off the seat, at least put your inside shoulder and head to the inside of the turn, and even a little forward. Once again, I can't emphasize a good quality track day enough. You will learn SO much, then you will want to go back as often as possible.
These things are not difficult to do, but it is very difficult and takes practice and discipline to stop your brain from panicking and doing the exact wrong things. THAT part is hard, but you can do it. Good luck.
One more thought......You can always speed up if you want to in the middle of a corner, but sometimes you can't slow down enough. Like was said earlier, slow in, fast out.
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