Cut two 8-inch circles from a clean plastic grocery store bag or gallon-size zip-top bag; set aside.
In a large bowl, combine the masa harina, 4 cups of the warm water, and the salt. Mix and knead with your hands until the dough is smooth and homogenous, adding more water 1/4 cup at a time as needed—the dough should feel like Play-Doh: flexible, soft, and smooth, not stiff. To test the dough, pinch off a bit, roll into a ball, and flatten between your palms. The dough should flatten easily, with few if any cracks forming around the edges. If deep U-shaped cracks form, add more water and test again.
Divide the dough into 2-oz. balls (about the size of golf balls), keeping them covered with a damp towel while you shape them.
Heat a large griddle over medium heat (or use two large skillets if you don’t have a large griddle). Use a tortilla press or the bottom of a wide, heavy pot to flatten a dough ball between the two pieces of plastic into a 6-inch tortilla of even thickness. Peel off the top piece of plastic, flip the tortilla over onto your hand, and carefully peel off the other piece of plastic.
Slap the tortilla onto the griddle (this breaks any air bubbles) and cook, flipping once, until the surface is brown in spots and appears dry, 1 to 2 minutes per side. While the first tortilla cooks, shape and begin cooking another. Continue shaping and cooking the remaining tortillas in this manner. As they’re done, wrap them in a slightly damp dishtowel to keep them warm and flexible.
You can make the tortillas up to an hour before serving. Wrap them in a clean, slightly damp dishtowel, and then wrap the towel in foil. Keep warm in a 200°F oven.