In a small bowl, dissolve the sugar or honey in warm tap water that is 110-115 deg F. (When making the New York Variation, omit the sugar and proceed as follows). Sprinkle the yeast over the water and stir gently until it dissolves, about 1 minute. Let stand in a warm spot until a thin layer of foam covers the surface, about 5 minutes. Discard mixture and start over if bubbles have not formed within 5 minutes.
If making whole-wheat dough, combine the 2 flours in a bowl and use as the flour in the directions that follow.
If making the cornmeal dough, combine the flour and cornmeal in a bowl and use the mixture as the flour in the directions that follow.
To mix and knead the dough by hand: Combine 3 cups of the flour with the salt in a large mixing bowl. Make a well in the center of the flour and pour in the yeast mixture and the oil, if using. Using a wooden spoon, vigorously stir the flour into the well, beginning in the center, and working toward the sides of the bowl, until the flour is incorporated and the soft dough just begins to hold together.
Turn the dough out onto a lightly floured surface. Dust your hands with flour and knead the dough gently in the following manner: press down on the dough with the heels of your hands and push it away from you, then partially fold it back over itself. Shift it a quarter turn and repeat the procedure. While kneading, very gradually add just enough of the remaining 1/4 c flour until the dough is no longer sticky or tacky. This should take about 5 minutes. As you work, use a metal dough scraper to pry up any bits of dough that stick to the work surface. Continue kneading until the dough is smooth, elastic, and springy. Too much kneading overdevelops the gluten in the flour and results in a tough crust.
After mixing and kneading the dough, shape the dough into a ball and place it in a well-oiled bowl, turning to coat completely on all sides with oil. Cover the bowl tightly with plastic wrap to prevent moisture loss and set to rise in a draft-free warm place (75-85 deg F) until doubled in bulk, about 45 minutes for quick rising yeast to 1 - 1.5 hours for regular yeast.
With your fist, punch down the dough as soon as it has doubled in bulk to prevent overrising. Shape it into a ball, pressing out all the air bubbles. If you are using bread flour or semolina flour, turn the dough in an oiled bowl to coat once more, cover again with plastic wrap and refrigerate it until puffy, from 35 minutes to 1 hour. Omit this step if using all-purpose flour.
If you cannot bake pizza withing 2 hours after rising, punch the dough down again, turn it in an oiled bowl to coat once more, cover the bowl tightly with plastic wrap and refrigerate. The dough can be punched down a total of 4 times and kept refrigerated up to 36 hours before the yeast is exhausted and the dough unusable. Let chilled dough come to room temperature before proceeding.
Excerpted from the book, _Pizza_, by James McNair. Chapter includes instructions on dough-making with a food processor and professional mixing bowl.