Why we don't touch the rolling pin
Okay so here's the thing. You've got dough that's fermented right, you've got a feel for it, and now you're standing over it with a rolling pin in your hand like it's a normal thing to do.
Put it down. We don't use those here.
Rolling pins are for pie crust. Pie crust wants to be flat and even and cooperative, and a rolling pin does that job fine. Pizza dough is a different animal. All that time in the fridge built up gas bubbles in there, little pockets of air the yeast made while you weren't looking. That's what gives you a crust with some life in it, some puff at the edge, some chew. A rolling pin flattens all of that back out. You'd be undoing three days of work with one pass of a wooden stick. Why would you do that to yourself.
So we stretch by hand instead. Here's how.
The actual method
Take your dough out of the fridge and let it sit at room temp for a bit first, thirty minutes to an hour, so it's not fighting you. Cold dough is stiff and it'll snap back every time you try to stretch it, which is annoying and also not the dough's fault, it's yours for skipping this step.
Flour your hands and the counter lightly. Not a blizzard of flour, just enough that things don't stick.
Press the dough down into a flat-ish disc with your fingertips first. Push from the center out, leaving maybe an inch around the edge untouched. That edge is going to be your crust and you want to leave it alone so it can puff up in the oven.
Then pick it up. This is the part that freaks people out. Drape it over your knuckles, or lay it flat on the backs of both hands, and let gravity do some of the work. Turn it slowly, letting the edges stretch down and out under their own weight. You're not yanking on it. You're rotating and letting it hang.
If it starts getting thin in one spot, move on to a different part of the dough instead of continuing to work that spot. That's the fix for most tears before they happen.
About the tears
You are going to tear one. Probably several, over time. First time I did this instead of reaching for a rolling pin, I put a hole clean through the middle. Tried to patch it by folding dough over dough, which just made a lumpy spot that cooked unevenly, and what came out of the oven was shaped like Idaho. Not round. Not even trying to be round. I ate it anyway, it tasted fine, but it looked like a state nobody would pick for a vacation.
That's the tuition. You pay it in torn dough and weird shapes until your hands learn what the dough is telling them. I still don't shape a perfectly round pizza, not after years of this. Mine come out looking like Idaho, or Ohio, or some country that hasn't been named yet. Yours don't have to be round either. Round is not the goal. Cooked evenly and tasting good is the goal.
If you tear one small hole, don't panic and don't try to patch it big. Pinch it shut gently with wet fingers, small pinch, and move on. A small patch disappears once it bakes. A big patch turns into a dense gummy spot because that area got worked twice as much as the rest.
Real talk about the rolling pin urge
I get why people reach for it. It feels more controlled. You can see exactly how thin it's getting, it's even everywhere, it looks like it's going to plan. That's exactly the problem. A rolling pin gives you a flat, dead-feeling crust because it pushes all the air out that the dough spent two or three days building up. You end up with something that bakes into a cracker instead of a crust with any texture to it.
My opinion, and you can disagree with me, but I've made a lot of pizza both ways: hand-stretched dough with some rough edges beats a perfectly even rolling-pin crust every time. The imperfection is where the good part lives.
A quick tangent about toppings, since we're here
My brother Blake dared me once to dunk a piece of leftover crust in fry sauce instead of ranch or marinara, and I won't pretend I didn't like it. I don't put that on any public forum because people act like it's a crime against Italy, but between us, it's good. Try it on your crust ends once you've got a stretched pizza baked. Don't @ me.
Watch your hands, not just the dough
If your dough sticks to the counter mid-stretch, don't rip at it. Lift a corner, add a little more flour underneath, and try again. Ripping while it's stuck to the counter is how you get a hole that's hard to fix, not the small forgivable kind.
Before next time
Try stretching one ball of dough by hand before our next lesson, just to feel what tearing feels like before we're all doing it together in class. Don't stress about the shape.