Kneading 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.
YouTube Video on Kneading
Kneading allows the dough to create a structure of gluten strands from the existing protein in the flour. Through hydration of the flour, enzymes bread down the protein to gluten and through light movement the gluten will form strands allowing the dough to trap the carbon dioxide created by the yeast to form the bread structure in your crust. The gluten strands are also crucial in allowing the dough to be stretched without tearing. With maximum development of the gluten strands you should be able to stretch you dough out paper thin.
Since your dough is undergoing changes during the kneading process the texture of it will start to change over the process. This change is more obvious if you are using high protein bread flour. After 6-10 minutes of kneading you should notice that the dough has a much smoother and elastic texture than previously.
To check the gluten development you can test by what is called the bakers window pane. This involves simply tearing a small piece of dough off and gently stretching it so it doesn’t tear. If you can see a web like structure when held up to light then the gluten has developed enough strands. If not keep kneading.
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.
Proofing can be divided into a couple of different stages; 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.
Fermentation proofing is typically the first stage of the proofing process. This is when the dough has been mixed with yeast and allowed to rise before final shaping occurs. This stretches the dough causing more gluten to align and also allows the dough to relax. The fermentation proofing will be finished when the dough has double in size or a bit larger, when poked the dough will retain the indention. If the indention bounces back then it needs to proof longer. The dough will collapse if it has fermented too long. In many recipes this is the longest the dough will proof and allows the yeast to impart its flavor into the dough. During this stage of proofing the dough should be kept around 70 to 80 degree fahrenheit, covered with a cloth or plastic and away from drafts. This process can be anywhere from an hour to six hours or maybe longer. Make sure you use a bowl that is larger than twice the size of the original dough ball to allow for expansion.
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 32 to 40 degree are appropriate for slowing down the fermentation rate of the yeast. The dough should be allowed to warm which takes about an hour after being removed from the refrigerator before use.
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.