How to cook a thin crispy pizza on a pizza stone

I agree with baka that the stone must be really hot--as hot as your oven can go (and completely preheated). To prevent sogginess, you need to cook the underside of the pizza as quickly as possible, so getting that strong, direct heat on there helps.

It also helps to use less sauce or a thicker sauce, and if possible, pre-cook or par-cook the vegetable toppings. Veggies release a lot of moisture when they cook, so if you get that out of the way beforehand, that can cut down on soggy crust. Another trick is to turn on the broiler just before you put the pizza in. This cooks the top faster and can help dry the toppings. But you have to be careful--if your stone isn't hot enough you can wind up with a burnt top and undercooked crust.

If none of that gets you what you want, you can also blind bake the crust a little: Put it on the stone for a minute or so before you put toppings on.

I should point out, though, that my sister has a real-deal brick pizza oven in her yard, and with that properly preheated, you don't need to worry about doing too many tricks to get the crust crisp (she does pre-cook watery vegetables like mushrooms). The air temperature in the oven tends to be more than 600 degrees, and the floor of the oven is at least that hot. Crisp crusts and melted cheese in about 90 seconds. So high temperature is crucial.

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".

As the other answers have said, preheating the stone is critically important, and you should make sure you're not putting a lot of watery ingredients on top.

To help with the "watery topping" problem, I usually spritz or brush the top of the dough with olive oil before putting on any toppings. It helps make a sort of moisture barrier that keeps too much water from seeping into the dough. Since the first thing I put on top of a pizza is roasted and crushed tomatoes, there's usually a lot of water to keep out.

Take a look at Kenji's recipe for bar-style pizza http://slice.seriouseats.com/archives/2011/04/the-pizza-lab-how-to-make-bar-pies-at-home-star-tavern-colony-grill-pepperoni-bar-pizza-recipe.html

There's some techniques worth reading in there. That's an A.P. flour pie, search for his NY-Style pie recipe for a Bread Flour recipe.

I've made two batches of the bar pie and it worked very well. I followed fairly precisely: few days in fridge, oiled pizza pan then onto a stone to finish.