Method 1: If using sourdough starter, mix the sourdough starter, water, sugar, and olive oil in a large bowl to prepare your wet ingredients. Mix well to combine. In a separate bowl, mix the flour and the salt together.Method 2: If not using sourdough starter, but using active dry yeast, mix the yeast, water, and sugar in a measuring cup and allow the yeast to dissolve and bubble up in the cup. Once the yeast mixture bubbles, add the mixture to a bowl and mix in the olive oil. Mix well to combine to prepare your wet ingredients. In a separate bowl, mix the flour and salt together.Method 3: If not using sourdough starter, but using instant yeast, mix the yeast with the flour and salt in a bowl. In a separate bowl, mix the water, sugar, and olive oil to prepare your wet ingredients. For all three methods above, add the flour mixture to your wet ingredients, and mix together until the dough comes together to form a ball and no longer clings to your large bowl.
Cover the bowl with the dough in it with a dish towel and allow the dough to rest for 30 minutes. This allows for the liquid to fully saturate the flour and the gluten strands to begin to form which will make kneading the dough easier.
After 30 minutes, place the dough on a flat surface. Avoid adding any extra flour. Begin to knead the dough for 8-10 minutes until it forms a smooth ball. (See video.) If the dough sticks to your surface, use a bench scrape or spatula to scrape it off the surface and re-incorporate it with the dough ball.
Return the dough to the empty bowl to which you have added some olive oil, turn the dough around in the oil to coat the bottom of the dough, and then drizzle some olive oil on top of the dough. Make sure that dough is well covered with olive oil. For Method 1: If using a sourdough starter, cover the bowl tightly with plastic wrap and refrigerate the bowl for 12-24 hours.NOTE: If you prefer to make a "fast" sourdough pizza crust, cover the bowl tightly with plastic wrap and then with a dish towel and and leave the dough to rest in a warm place for 2 hours. This will create a less "sour" sourdough crust and may give a more familiar taste for those new to sourdough. For Method 2 and Method 3: If using commercial packaged yeast, whether it is active dry yeast or instant yeast, you don't have to refrigerate the dough. Instead, cover the bowl with plastic wrap and then with a dish towel. Allow dough to rise in a warm place for 1 ½ hours.
For Method 1: If using a sourdough starter, remove the pizza dough from the refrigerator after 12-24 hours and allow the dough to come up to room temperature. This warming process will take approximately 1 hour.
Place your oven rack in the middle of the oven, and place the pizza stone on the oven rack, if using one. Preheat the oven to 475°F.
Next, regardless of what method you have used to rise your dough, once the dough's rise time has completed, punch down the dough to deflate it, and transfer the dough to a floured board. Cut the dough into two equal pieces, and put one piece back into the bowl. Begin to flatten the piece of dough on the board, and shape the dough into a round disc that's approximately 10-12 inches in diameter. You can do this with your hands by stretching the dough or you can use a rolling pin. (See the video for the technique.)
Once shaped into a round disc, transfer your dough to the pizza peel. If you are using the baking sheet pan, turn it upside down and place your pizza dough disc on the underside of the pan. If using aluminum foil, use three sheets of foil to create a makeshift baking sheet pan and place your pizza dough disc on the aluminum foil. You can also shape your round dough discs on these surfaces, if it is easier for you and enables you to avoid having to transfer the round disc to the baking sheet or aluminum foil.
At this point, you can put the toppings on your pizza dough. You can make a simple cheese pizza by spreading about a cup of tomato sauce on top of the dough, making sure you have a one-inch border without sauce within the edge of the crust. Next, sprinkle the pizza with cheese. (Be sure to add pepperoni if you're making a pepperoni pizza pie!)Place the pizza into the oven and bake for approximately 20 minutes until the crust is golden brown and the cheese is bubbling. Continue the same steps to create your disc with the second ball of pizza dough.