In a small bowl, combine the warm water, sugar, and yeast. Let it sit for about 5 minutes until the yeast becomes frothy. In a large mixing bowl, whisk together the flour and salt. Make a well in the center and pour in the yeast mixture and olive oil.
Stir the ingredients together until they start to come together, then transfer the dough to a floured surface. Knead the dough for about 5-7 minutes until it becomes smooth and elastic. Add a little flour if the dough is too sticky.
Place the dough in a greased bowl, cover it with a clean kitchen towel, and let it rise in a warm place for about 1-2 hours or until it doubles in size. Preheat your oven to the highest temperature setting (typically around 500°F or 260°C) and place a pizza stone or baking sheet in the oven to heat up. Punch down the dough to remove any air bubbles, then divide it into two equal portions. Roll out each portion into a thin round shape to fit your pizza stone or baking sheet.
Carefully transfer one of the rolled-out dough rounds onto a piece of parchment paper. Spread a thin layer of tomato sauce onto the dough, leaving a small border around the edges. Sprinkle a generous amount of shredded mozzarella cheese over the sauce, and add your desired toppings.
Carefully transfer the pizza (with the parchment paper) onto the preheated pizza stone or baking sheet in the oven. Bake for about 10-12 minutes or until the crust is golden brown and the cheese is melted and bubbly.
Remove the pizza from the oven and let it cool for a few minutes before slicing and serving. Repeat the process with the remaining dough and toppings to make the second pizza