It is important to have a hot stone in the oven or on the grill first. Then, slide the pizza onto it to get the crispiest crust. Sliding the pizza onto the stone can be challenging. Here are some tips that might help. When making your pizza, dust the counter with enough flour so that the bottom of the pizza is not stuck to the counter. If you can slide it around on the counter, then it will slide onto the hot pizza stone. I have used five different tools to transfer the pizza to the hot stone.
When I first started making pizzas, I used a clean piece of stiff cardboard or the bottom of an old pizza box. I dusted the surface of the cardboard with some corn meal. I made sure that I had my thin dough lightly floured, so it would lift and slide around on the counter. Using a wide spatula, I lifted one edge of the pizza as a I slid the cardboard under the pizza. I gently worked the cardboard all the way under the pizza. I then lightly dusted my hot stone with cornmeal and slid the pizza from the cardboard directly onto the hot oven. Taking the pizza out of the oven when it is done is easier because the crust is nice and crisp. I use the wide spatula again to gently lift an edge and slide the pizza from the hot stone to the cardboard.
I have recently changed my technique and started just leaving the pizza on the stone and bringing it all onto the counter. I serve the pizza from the stone, and it stays hot while we eat it.
Method 2 is easier in some respects. I use a cookie sheet in place of the cardboard. I have one that has a flat edge with no lip. Again, flour the surface that the dough rests on so that, after kneading and rolling, the dough is not stuck to the surface and can be easily slid around. The same steps as above apply. You can also just roll the dough out directly on a floured cookie sheet.
Method 3 is downright cheating. I make the pizza on parchment paper and then put the whole thing in the oven on the hot stone. When it is finished, I just pull it all off onto a cookie sheet. The big advantage of this is there is no mess to clean up. Please do not tell anyone about this. The pizza purists will revolt.
Method 4 requires justification. After making a zillion pizzas, I justified (in my own mind, at least) that I should buy a pizza peel. Pizza peels follow the same procedure, but are easy to handle and are more forgiving. You still must get the dough “floured” enough to move and slide, but that is easy once you get the hang of it.
Method 5 is what professionals do. They make the pizza on a pizza peel or a flat sheet of metal that has been floured or has corn meal on it. They dust the stone with corn meal and slide the pizza off onto the hot stone. The dough has been well-floured, so it is readily moveable.