This is the recipe I use for normal pizza dough. If provides a medium-rise crust, not the Rome-style cracker crust, nor the thick, coarse dough of a deep dish. It can be used for regular pizzas or calzones. It makes enough dough for 2 big pizzas, sometimes with a bit leftover. Adjust the water up or down to change the dough size.
Warm water - 1.5 cups
Active dry yeast - 2 teaspoons
Sugar - 1/4 teaspoon
Salt - 2 teaspoons
Olive Oil - 1 tablespoon
Extra strong bread flour - 4 - 6 cups
Proof the yeast by combining 1 cup of the warm water with 2 tsp yeast, 1 Tbls flour and 1/2 tsp sugar. Stir to dissolve the yeast and set aside till foamy on top, up to 10 minutes.
Add the remaining 1/2 cup warm water, approx 2 cups of flour, 2 tsp salt, 1 Tbls olive oil. Adjust the flour amount to keep the consistency at a thick batter, not a dough yet. Beat well for a few minutes with large wooden spoon. Alternately this can be done in a mixer at medium speed for 5 minutes with a paddle attachment.
Now to finalise the flour by beating in smaller amounts of flour until a fairly wet dough consistency is achieved. If done in the mixer it will pull away from the sides and start to form a ball.
Now knead the dough on a well-floured surface for at least 10 minutes, adding flour as needed to keep it from sticking to you and the surface. This also can be done in a mixer with the dough hook. Dough should be smooth and elastic.
Roll into a ball and toss with a teaspoon of olive oil in a bowl to coat. Loosely cover with cling wrap and let sit in a warm place to rise for about an hour until doubled in size.
Divide into pizza portions (about 350-400g for a large pizza that fits out peel), re-shape into balls and set aside for a second short rise, at least 15 minutes, preferably 30.
Stretch and use. For me that is on a ceramic pizza stone in the lowest part of the oven and the highest heat I can get the oven to.
The overall idea is to keep the dough as wet as possible, but not so much that it is too sticky to work with. Traditionally the whole process would be done in a "well" formed in a big pile of flour, letting the dough take up all the flour it needs during the mixing process.
Kneading allows the gluten to develop in the dough, providing a strong matrix to contain the CO2 expelled from the yeast and enable rising. The strong bread flour has a higher concentration of protein (e.g. 12g/100) that normal to help this. The longer you kneed, the more develops (up to a point apparently). Longer machine-kneading is used for commercial doughs. The ideal is to aim for the "window pane" membrane in the dough, though I've never achieved it...
Rising is dependent on the amount of live yeast(+), salt(-) and ambient temperature(+). Traditionalists go for less yeast (1/2-1 tsp) and a long, slow rise. AB even suggests an overnight rise IN THE FRIDGE!
The second rise, after shaping into individual balls allows the gluten to "relax" and makes the dough easier to stretch. If you are having trouble with it springing back to much, let it rest some more.
Medium-term storage is possible in the fridge as individual balls. The yeast will live slowly at lower temps. Eventually they will use up all their food and die, but that should take several days. Bring them back to room temperature before stretching. I've had no success with freezing, I think it kills the yeast, but others on the web differ.
Alton Brown's Good Eats - overnight fridge development.
Pizza Perfect - overnight fridge development.
Forno Bravo Pizza Ovens - good info on resting