The process for making pizza starts the same as for bread. Follow that process up through the bulk fermentation.
Neapolitan style pizza uses a very thin crust, and it's helpful to have a dough that's a bit stronger than for normal bread. For pizza I'll use all white flour, preferably high gluten, and even OO if I can find it. A somewhat lower hydration will make the dough easier to work with and less apt to fall apart.
Split off the portion of the dough to be used for pizza. Cut this 500g flour worth of dough into thirds.
Shape each chunk into a tight ball the same way you would for a boule of bread. They need the strength.
If you have round shallow bowls or food containers that are about the right size for individual balls of dough, that's best. Otherwise you can store all the balls together in a shallow pan - oil will keep them from sticking together.
Oil each dough ball all over, place in the containers and seal with a lid or plastic wrap. Place in the fridge 12 - 24 hours.
I like to do the above steps in preparation for a pizza night with friends. When they come over, we can stretch the dough out, top it, and bake it, eating the pizzas as they come out of the oven. Three pizzas is usually enough for four people.
Preheat the oven to 500°
It's hard to get a home oven to produce a decent pizza. At a minimum, you'll need a baking stone, though baking steels work better. Search around for options. Preheat whatever you're cooking on too.
You'll need something thin to transfer the pizza in and out of the oven. A pizza peel is ideal, a cutting board will work, but the thickness makes things harder. I've heard of people using cardboard.
You can make the pizza on a countertop or directly on your peel. Generously flour your work area, dump the first ball of dough onto it, and flour the top of the dough too. Do not fold the dough. Flatten the middle of the dough with your hands. Flip it over a few times to make sure it's even and that there are no oily spots.
There should be gas trapped in the dough - your goal is to de-gas the sauced part of the pie, but not the rim. Avoid touching the rim as much as possible. Pick up the dough and stretch it over your knuckles, gently working it bigger. You can let it rest for a minute if it's not stretching easily. It should be about a foot across and nearly translucent in the middle.
Make sure there's plenty of flour under the dough so it doesn't stick while you top it. Spread the sauce over the dough, then top with decent mozzarella and whatever else you're using.
Quickly slide the peel under the dough, or if you prepared it on the peel, give it a shake to make sure the pizza is loose. Put the peel to the back of the baking surface, shake the pizza until it starts to slide off and touch the stone, then jerk the peel out from under it quickly. You have a few seconds to try to rearrange the dough with a spatula if it went poorly.
This should bake quickly. Lift up the dough with a spatula to check the bottom. When it's about done, you can turn the broiler on for 30 seconds or so to blast the top.
If you have a peel, you can just slide it under the pizza, otherwise use a spatula, fork, or tongs to slide the pizza off the stone onto a cutting board.
Drizzle a little olive oil over the pizza, slice it, and slide it onto a wire rack so the bottom doesn't go soft. Eat immediately.
Use decent mozzarella. Slice it thick, then tear each slice into chunks. That and fresh basil makes a damn fine pizza.
Other choice toppings include: