Have a tortilla press or heavy small cast-iron skillet. Cut a rectangle 6 by 6 inches out of a quart size plastic freezer bag, Open it and cut a minimum of an 18 by 9-inch rectangle. Open the press and lay plastic across both surfaces, creased edge next to the hinge. Keep rectangle nearby if not using a press.
Add fresh masa or masa harina & water dough to a large bowl. Work masa with your hands. It should feel like a stiff cookie dough. If not pliable enough, work-in 2-4 tbsp water. With wet hands, roll dough into 10-12 ping-pong sized balls and cover them with a damp cloth.
Heat a griddle or cast-iron skillet over high heat. Grease griddle with a vegetable oil moistened paper towel rubbed over the surface. Place a dough ball in the center of tortilla press between the 2 flaps of plastic (see notes for non-press method). Lower the top of the press and push the handle down to form a 5-5-inch round tortilla, 1/16-inch thick. Open the press and peel off the top flap of plastic. Lift out the tortilla a peel away the bottom flap.
Place the tortilla on the hot griddle or skillet. Cook about 1½ minutes. Tortilla should be lightly flecked with brown on the underside. Turn with a spatula and cook for another 1½ minutes. It should puff up slightly at this point. Turn once more and press it down. Remove to a plate and cover snugly with a towel. Repeat until no more dough balls, stacking and covering them as they are done.