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.