Special equipment: a pizza stone and pizza peel or 2 baking sheets
For the pizza dough: Add the warm water in a small bowl and sprinkle over 1 teaspoon of the sugar and the yeast; set aside so the yeast can proof.
Oil two bowls with a little olive oil and set aside.
In the bowl of a stand mixer fitted with a dough attachment, mix together the olive oil, salt, 3 1/2 cups of the flour and the remaining 1 1/2 teaspoons sugar. Stir the yeast in the water to make sure it's all dissolved and add it to the flour mixture. Mix on medium-low speed until everything is combined. Increase the speed to medium and allow the machine to knead the dough, adding more flour if necessary, until it is smooth and comes away from the side of the bowl, 6 to 7 minutes.
Divide the dough in two pieces and roll each into a ball. Place a ball in each of the oiled bowls seam-side down, and brush the tops with a little oil to stop them from drying out. Cover the bowls with plastic wrap and place in a warm place (inside a microwave or a turned-off oven works best) until it doubles in size and when poked with a finger, the indent remains (it doesn't spring back), about 1 1/2 hours.
For the margherita pizza: Place a pizza stone in the oven and preheat the oven to 475 degrees F. If you don't have a pizza stone you can use a large baking sheet turned upside down.
In a small bowl, mix together the strained tomatoes, olive oil and salt; set aside.
Sprinkle some flour onto your counter. Take the remaining ball of dough and dredge it in the flour on all sides. (Reserve the remaining ball for another use; store in the refrigerator for up to 24 hours.) Using your hands or a rolling pin, roll the dough out to a 10-inch circle and place it on a semolina-dusted pizza peel or an upside down baking sheet. Ladle on your tomato sauce.
Slide the pizza onto the pizza stone. Bake the pizza until the crust is cooked and beginning to brown slightly, about 10 minutes. Remove from the oven, scatter your fresh mozzarella over the top and pop it back in until the cheese is melted, 3 to 5 minutes more. Remove from the oven, sprinkle over a pinch of dried oregano, scatter the basil leaves and drizzle with a touch of olive oil.
You can use store-bought pizza dough instead of homemade. If you can't find the San Marzano variety of strained tomatoes, you can use San Marzano whole peeled tomatoes and puree them in a food mill or food processor.