Combine the dry ingredients. Add the flour, instant yeast, salt, and sugar to a large mixing bowl or the bowl of a stand mixer. Whisk until evenly combined.
Add the water and olive oil. Make a well in the center of the flour mixture. Pour in the olive oil and warm water, then stir with a wooden spoon or sturdy spatula until a rough, shaggy dough forms.
Knead the dough. If using a stand mixer, attach the dough hook and knead on medium speed for 7-8 minutes, or until the dough is smooth and elastic. To knead by hand, transfer the dough to a lightly floured surface and knead for 10-12 minutes. The dough should be soft and slightly tacky, but not wet.
Let the dough rise. Lightly oil a clean bowl. Add the dough and turn it once to coat the outside with oil. Cover with a clean kitchen towel or plastic wrap and let it rise in a warm, draft-free place for about 1 hour, or until doubled in size.
Divide and shape. Gently punch down the dough to release the air. Transfer it to a lightly floured surface and divide it into 8 equal pieces. Shape each piece into a smooth ball.
Roll the pita. Use a rolling pin to roll each dough ball into a circle about 1/4-inch thick and 6-7 inches wide. Keep the thickness as even as possible. Cover the rolled pita rounds with a clean towel and let them rest for 15 minutes.
Cook on the stovetop. Heat a cast-iron or nonstick skillet over medium-high heat until very hot. Place one pita round in the skillet and cook for 1-2 minutes, or until bubbles form and the bottom is golden brown. Flip and cook for another 1-2 minutes. Transfer to a clean kitchen towel and cover to keep warm. Repeat with the remaining dough.
Or bake in the oven. Preheat the oven to 475°F with a pizza stone or heavy-duty baking sheet inside. Carefully place 1-2 pita rounds on the hot surface and bake for 3-4 minutes, or until puffed and lightly golden. Remove right away and wrap in a clean kitchen towel to keep soft.