Kneading the Dough
Kneading dough is done by stretching the dough in one direction till it is about double the length it was then folding it in half. Rotate 90 degrees and repeat. You will not want to stretch the dough to the point where it is starting to tear as this is causing gluten strands to break. The below YouTube video demonstrates how this is done.

Kneading Test: Bakers Window Pane
Proofing Pizza Dough
What is Dough Proofing?
Proofing or simply allowing the dough to rise is giving time for the yeast to convert the sugar, glucose, to carbon dioxide and alcohol. The carbon dioxide causes the increases in volume of the dough and the alcohol byproduct gives flavor to the bread. Proofing is important to the formation of flavor in your dough as well as developing aligned gluten chains to trap in carbon dioxide leaving a light and airy final product.
Stages of Dough Proofing
Proofing can be divided into a couple of different stages; bulk fermentation, retarding and shape proofing. Typically the fermentation and shape proofing is used in most pizza dough creation although if time permits retarding will allow more flavor to develop.
Bulk Fermentation of Dough
Retarding Dough
Retarding is cooling off the dough to slow down the fermentation rate. This allows more complex flavors to be created and also will allow you to be able to make dough the day before you need it. In the home the refrigerator is the best place to accomplish this. For pizza dough I prefer to shape the dough into balls prior to putting in the refrigerator so they will be one step closer to being ready to use when you take them out of the refrigerator. Temperatures from 33°F to 40°F (1°C to 4°C) are ideal for slowing down the fermentation rate of the yeast for a very slow extended fermentation. The dough should be allowed to warm which takes about an hour after being removed from the refrigerator before shaping for final proofing.
Shape Proofing Dough
Shaping proofing is the final stage of proofing. Traditionally this is allowing the dough to rise in the shape you will bake it in. For pizza dough this stage will be shaped into individual balls to allow them to easily be stretched into flat discs without forcing out all of the trapped air.