I have had this problem in the past myself. There are 4 main factors involved:
Technique - You have to use a very fast and smooth movement. Sliding the edge of the pizza off the peel onto the stone, allowing the pizza to catch the hot surface as you slide the peel out from underneath.
Dough - The dough needs to have enough gluten developed to keep from ripping easily. You can make a really thin dough, as long as it has enough gluten, it shouldn't rip. There are 2 ways to develop gluten, working the dough or time. So take a tip from the pros and let the dough rest overnight, most pizza places do. Also make sure to use a good high gluten flour to begin with.
Time - The amount of time the pizza is on the peel with give the moisture extra time to soak into whatever you have underneath the pizza. If it's flour, it will soak up pretty quickly and cause it to stick, also depending on the moisture content of the dough. Work quickly and shake the peel often to make sure there is no sticking.
Peel - There are many different times of peels out there, but wooden is the way to go. With a porous structure there is less contact with the pizza dough as the surface isn't completely smooth. Metal tends to stick more. You can use just about anything to dust the peel, traditionally flour, but if that doesn't seem to work, you may want to try cornmeal or even rice flour.
I used to have a tough time with the dough myself, and though I still haven't found the right recipe or ingredients to make that pizzeria style pizza, I'm enjoying all the practice!