How to cook a thin crispy pizza on a pizza stone
The most important thing is for the stone to be hot.   That generally means you need to set the oven to its highest setting, and then let it preheat for at least 30 minutes.   

I use a 1-inch thick paver from a hardware store, and I generally get my best pizzas when I set the oven to 500F and wait about 45 minutes before I put the pizza in.

For a thin crust, I like the results from leaving the oven at 500F and baking for ~13 minutes in my oven, but I'm sure some people would consider that "burned".