Punch down the dough and shape into a log about 8-10 inches long. You want the log to be pretty round.
On a lightly floured board, slice the dough log into 8 even pieces. I like to cut the log in half, then cut each of those in half, then cut the four pieces in half. I find it's easier to get the slices even that way.
Gently flatten each of the 8 dough rounds on the lightly-floured board. Cover with a kitchen towel so the rounds don't dry out as you work with them.
Preheat the oven with the pizza stone inside to 490 degrees F while you press the dough.
Cut two pieces of parchment paper to the approximate size of the tortilla press.
Place one piece of parchment paper on the bottom of the tortilla press. Lightly dust the parchment with flour and place a dough round on top of the parchment. Lightly dust the dough round with flour and place the other piece of parchment paper on top of it.
Put the top of the tortilla press down and use the handle to flatten the dough. You don't need to use a lot of force--you'll be pressing it several times.
Open the tortilla press and turn the dough (and its plastic) 180 degrees, so the part that was next to the handle is now next to the hinge. Press again.
Turn the dough and parchment 90 degrees and press again. Then turn 180 degrees again and press. Now you've pressed the dough in all four directions and the dough is between 1/16" and 1/4" or 1.5 and 3 mm thick.
Peel the plastic off the dough and place the pressed round back on the lightly floured board. Cover with a towel to prevent the dough from drying out.
Repeat the pressing process with the other dough rounds.
When the oven is hot, place a dough round on the pizza stone and close the oven. Set a timer for 3 minutes. Watch the pita carefully. If your dough is thin and puffs completely, remove it from the oven and on to a cooling rack as soon as it finishes puffing. If you dough is thicker and it doesn't visibly puff up, flip the pita after about 2 minutes and continue baking for one minute more, then remove from the oven to a cooling rack. (Don't worry, you should still have a nice pocket when the pita is done.)
Repeat the baking process with the rest of the dough rounds. When you get the hang of it, you can bake several at a time. My pizza stone is large enough for me to bake four at a time.
Allow the pitas to cool completely before using or storing.