In a medium bowl, combine the masa harina and salt with 1-1/4 cups warm water. Mix and knead with your hands until the dough is smooth and homogenous. It should be soft but not sticky, like soft Play-Doh; if necessary, adjust the texture with more water or masa harina. Cover with plastic and set aside at room temperature for at least 30 minutes and up to 2 hours.
Cut two squares or rounds of heavy plastic (from a ziptop bag or a plastic grocery bag) to fit the plates of a tortilla press. Set a large flat griddle on the stove, straddling two burners. Turn one burner on medium low and the other on medium high. (Use two skillets if you don't have a large griddle.)
Pinch off a golfball-size piece of dough and roll it into a ball. Cover the bottom plate of the press with a sheet of plastic and put the dough ball in the center. Cover with the other sheet of plastic and press with your palm to flatten slightly. Close the press and firmly push down on the handle. Rotate the tortilla one-half turn and press again. Repeat if necessary until the tortilla is an even 1/16 inch thick.
Peel off the top sheet of plastic, flip the tortilla over onto your hand, and carefully peel off the other plastic sheet. (If the tortilla breaks, the dough is too dry; if it sticks, the dough is too wet.)
Lay the tortilla on the cool side of the griddle by quickly flipping your hand over the griddle. Cook just until the tortilla loosens from the griddle, 15 to 20 seconds (if the tortilla bubbles, the heat is too high).
With a spatula, flip the tortilla over onto the hot side and cook until the bottom is lightly browned in spots, about 20 seconds more.
Flip again so the first side is on the hot part of the griddle and cook until the tortilla puffs in spots and browns lightly on that side, about 20 seconds more (if it doesn’t puff, the griddle isn’t hot enough, the dough is too dry, or you cooked it too long on the cool side). Immediately wrap the tortilla in a clean, dry cloth.
Repeat pressing and cooking the remaining dough, stacking and wrapping the finished tortillas in the cloth. Once they're all cooked, let them rest in the cloth for 10 to 15 minutes before serving. During this time, they'll steam themselves, becoming soft and pliable. You can also wrap the cloth-wrapped stack in foil and keep warm in a 200°F oven for about an hour.
Well-wrapped tortillas keep in the freezer for up to a month. Thaw overnight in the refrigerator and reheat before using.