Kenji over at Serious Eats gives some of the best "pizza science" lessons on the Internet. Here's a good article on the role of yeast and fermentation in pizza dough:
In short, time and kneading cause proteins in dough to form an elastic network of fibers called gluten. Yeast consumes starch and emits carbon dioxide. Gluten traps the carbon dioxide which causes the dough to expand or "rise".
The amount of yeast and time may vary based on the intent of the cook. More time allows the cook to use less yeast (the yeast organisms will multiply) and allows for a greater development of the proteins in the wheat flour.
A longer, slower rise will allow for the greatest flavor to be developed. In his tests, Kenji found the optimum rise time to be 2-3 days in a refrigerator. However, this must be balanced against the cook's desire for an expedient dinner :-)
In my personal pizza cooking, I usually use 1 packet of yeast (2.25 tsp) for approximately 13 cups of flour. I will typically allow this to rise for around 24 hours on my kitchen counter-top (my house says cold at around 55-60degF). If the dough will not be used right away, I will put it in the fridge but will allow it to warm to room temperature for several hours before cooking it.
Good luck with your pies!