In a large bowl, combine the flour, yeast, salt, and sugar. Stir with a wooden spoon or dough whisk until everything is mixed together.
Pour in the warm water and stir with the wooden spoon or dough whisk until a shaggy dough forms and there is only a little bit of dry flour at the bottom of the bowl.
If you're wearing any rings on your fingers, take them off. Knead the dough in the bowl with both hands until no more dry flour remains in the bottom of the bowl and the dough comes together into a ball. Start by poking the dough with your fingertips and squishing it through your fists, and then, when the dry flour is incorporated, keep folding and pressing it down with the heel of your hand until the dough doesn't stick to your hands and stays together in a smooth-ish ball. (This whole process should only take a few minutes.)
Grab a large bowl (preferably one that has a lid) and drizzle in some olive oil to coat the inside. (Or, you could clean the bowl you made the dough in and use that.) Place the dough ball in the greased bowl, cover tightly with the lid or plastic wrap, and put it in a warm place to rise for at least 45 minutes or up to 2 hours. (In the winter when my kitchen is chilly, I let the dough rise on the floor or on a chair near the radiator.)
Check your dough after 45 minutes. It should have puffed up and grown by at least 50 percent to fill out the bowl; on a warm day, it will probably have doubled by now, and there will be little bubbles on the bottom. You can ball up the dough and use it now, or you can let it rise for another hour or so to get a slightly airier dough.
Dust a clean work surface lightly with flour. Divide the dough into two equal pieces, and form each piece into a ball by stretching the edges underneath and grabbing the bottom of the ball with your fist. Place the dough balls on your floured work surface and cover with an inverted bowl or a piece of plastic wrap. Let rest for 10 to 15 minutes or until the balls puff up a bit. (If you're in a hurry, you can skip this extra resting time and roll out the dough balls right after you form them.)
To stretch/roll out the dough: Grab one dough ball and place it on a lightly floured surface. Set the other dough ball aside, still under the bowl so it won't dry out.
Flatten the dough a little with your hand or a rolling pin. (This will help keep it even as you stretch or roll it out.) Pick up the dough disk and tug gently on one side. If it gives easily, then you should have no problem stretching it out: keep turning and tugging gently on the edges, letting it hang from your forearm to let gravity do its work, and gently moving your fist underneath from the center to the edges until you have a 12-inch round. If the flattened dough disk barely gives at all when you give it that first tug, you might be better off rolling it out instead.
Finito! Top and bake the dough, then repeat the stretching or rolling process with the second ball of dough and top and bake that one, too. (Or, if you're only making one ball of dough, you can freeze the second ball in a zip-top bag or refrigerate it in an airtight container for up to 2 days (just make sure you thaw it out and let it come to room temperature before stretching).