Lightly spoon masa harina into dry measuring cups; level with a knife. Combine masa harina and water in a large bowl, stir well. Turn dough out onto a surface lightly sprinkled with masa harina; knead lightly 5 times or until soft (the consistency should be like soft cookie dough but not sticky). Divide dough into 12 equal portions. Shape each portion into a ball.
Working with 1 portion at a time, place dough between 2 sheets of plastic wrap (cover remaining balls to prevent drying). Place ball, still covered, on a tortilla press. Close press to flatten dough, moving handle from side to side. Open press; turn dough one-half turn. Close press to flatten. Remove dough. Carefully remove plastic from dough.
Place a nonstick skillet over medium heat. Add dough, and cook 15 to 30 seconds or until tortilla releases itself from the skillet. Turn tortilla; cook 30 seconds or until brown spots form. Turn again; cook another 30 to 45 seconds. (At this point, most of the tortillas will puff like pita bread.) Remove from pan. Keep warm. Repeat procedure with remaining dough.