Make the dough: Put the masa harina in a bowl and gradually stir in 1 cup plus 2 tablespoons warm water with a fork.
Add 3 or 4 more tablespoons water, 1 tablespoon at a time, and mix with your hands until the dough comes together.
Roll the dough into Ping-Pong-size balls, moistening your hands with water to keep the dough from sticking. Place the balls on a baking sheet lined with plastic wrap; keep covered with more plastic as you roll the rest of the dough.
First, set a large griddle over two burners; heat one side to medium-low and the other to medium-high (or use two cast-iron skillets).
Cut a circle slightly larger than your tortilla press from a large resealable plastic bag; include the seam of the bag in your circle so that the two circles remain attached on one side.
Place a dough ball between the plastic rounds and flatten in a tortilla press into a 5-inch circle, about 1/8-inch thick. (If you don't have a tortilla press, use a coffee can to flatten the dough.)
Peel off the top piece of plastic; flip the tortilla onto your hand and peel off the bottom piece of plastic.
Ease the tortilla onto the cooler side of the griddle and cook until it is slightly dry around the edges and starts to peel away from the griddle, about 45 seconds. Transfer to the hotter side of the griddle, uncooked-side down. Cook until speckled on the bottom, about 1 minute, then flip and cook until puffed in spots, about 1 more minute. Press and cook the remaining tortillas; stack them in a cloth-lined basket and cover with the cloth, or wrap in foil and keep warm in a 250 degrees F oven.