Inside there is a little screw that seems like it should attach to the stem coming from the wall. However, the head of the little screw is covered by the big cap on the end of the knob with the little indentation (you can see it in the picture).
It does push on, but then it won't stay on. Inside the cap is a little screw that has something to do with it staying on I'm sure. I can push it on and use it to turn the water on and off, but then it pulls right off.
Thanks for the suggestions. I'm still trying to get it figured out. I've looked at the diagram I found for what I think is my actual knob, http://www.us.kohler.com/onlinecatal.../1097384_5.pdf but I'm still not much farther along. The screw in my diagram is actually attached to the handle, can't tell how to get it out.
Redwood, thanks for your link, but that diagram looks like it goes to a control with a handle sticking out, where as mine looks more like the one in the link I put here.