Sift the flour, yeast, salt, and sugar together. Make a well in the middle of the dry mixture. Pour in the lukewarm water. Mix by hand on a floured work surface until the dough comes together. Then knead the dough for 10 to 15 minutes until smooth and the dough bounces back when you push into it. Drizzle the dough with olive oil and place in a warm spot covered with a damp towel. Let rise until the dough doubles in size; depending on the temperature, it could take 30 minutes to 1 1/2 hours.
Preheat the oven to 500 degrees F and lay a baking tray in the oven to heat.
Once the dough has doubled in size, cut the dough into 10 to 12 pieces. Roll each piece into a ball and then flatten each using a rolling pin. Use flour on the work surface so that it doesn't stick. Place 3 to 4 flattened pita on the hot tray and close the oven door immediately. Bake until puffed up, about 5 minutes. Remove from the oven and serve immediately.