In a small bowl, combine the masa harina and water, then knead until smooth, adding more water if necessary to achieve a soft, claylike consistency.
Prepare 5 pieces of parchment the size of your tortilla press. Place one piece on the bottom of the press. Place a ball of dough about the size of a walnut on the parchment. Cover with a piece of parchment, close the top plate, and press down firmly with the handle. Rotate the tortilla and press again, if necessary, to flatten the tortilla to a 1/16-inch thickness. Open the press, peel the top piece of parchment off the tortilla and reuse for remaining dough. Repeat with the remaining dough. Stack the tortillas on top of one another and cover the stack with a damp kitchen towel.
Heat a dry cast-iron skillet or nonstick pan until moderately hot. Hold one tortilla in your hand, peel the parchment away, lay the tortilla in the skillet, and cook 30 to 45 seconds per side. Repeat with the remaining tortillas, stacking them as you go. Serve immediately.