The version I am going to outline in this instructable is what I was taught by my teacher in grad school. I have not tried comparing it to other tempera techniques. If you would like to learn some other ways of doing this, you can visit www.eggtempera.com.
You can also find some history of egg tempera painting on Wikipedia.
Step 1: Why egg tempera?
Personally I have never ground my own pigment. I prefer to use watercolor that is available at art stores for coloring. This color variety is plenty for my needs.
If you decide you don't want to use watercolor, and prefer to grind your own pigment, you might want to do a search to find the right way to process the materials.
If you would rather experiment than research, cool! But remember, WEAR A RESPIRATOR when grinding pigment. Things that aren't usually dangerous can become poisonous if ground to a super-fine powder and inhaled.