The key is just that, a half moon shaped key that sits in the keyway on the crank and in the flywheel. It makes sure the flywheel can only be installed one way and timed correctly. Keeps it from moving as well. You'll see when you get it apart, it's super simple.
I bought a flywheel puller from the local dealer for 8 or 9 bucks. Handy to have around, and the model that fits the KDX's fits almost every other 2 stroke bike on the planet. I had mine on and off several times last year, had no problem with just putting the bike in 6th gear and holding the brake while turning the puller with a rachet.
PS, make sure you mark the timing on the plate after you pull the flywheel. If you are putting in a new stator and turn the plate (it has some amount of adjsutment for timing) you can change the bikes performace quite a bit, in a bad way.