This needs to happen quickly—in a mere two to three minutes—so don’t go running off when the pitas are baking. As soon as they puff, they’re done. Over-baking will leave them hard and dry.
If you don’t own a baking steel or stone, you can bake the pitas in a cast iron skillet instead. After rolling out the pitas, try not to tear the dough before baking. Doing so can create a weak point that may fail as the pita puffs, preventing it from fully expanding. Notice that the pita on the left here, which went into the oven with a slight tear, isn’t puffing like the other: Over the course of years of making pitas, I began to notice a tendency for the pita to end up with a much thinner top than bottom after it comes out of the oven. Eventually, I realized that this has to do with pockets of air rising to the surface of the dough during the final proofing step.