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.
Step 2: Tools and Materials
Pigment (We'll be using watercolor.)
A container (I used a cup. Probably not the best idea considering some watercolor paints are poisonous.)
Something to mix paint on (aluminum foil, wax paper, etc.)
Something to paint on (wood, paper, cardboard, etc.)
A slotted spoon (optional)
Paper towel (for cleaning up spills and drying brushes)
Step 3: Seperate the Egg Yolk
The other way is to filter it through your fingers by passing the egg back and forth gently from one hand to the other. It just depends on you and your level of comfort with gooey things.
Either way, be careful not to break the yolk sack. What you want is a pretty golden-yellow blob.
Step 4: Mix in Vinegar and Water
I was told the proper measurement is 1/2 eggshell of vinegar, and 1/2 eggshell of water. I did it with the eggshell, which leaked vinegar all over me. No surprise there. Next time I'll use a teaspoon. I think the idea is to just slightly cover the top of the yolk, so it isn't exposed to the air.
NOTE: On eggtempra.com the technique is a bit different. They don't use vinegar, probably because it is acidic and I think that can effect the archival quality of the artwork.
Step 5: Adding Pigment
The way we were taught to use the egg medium is to pierce a small hole in the yolk with the brush bristles. Now the bristles have eggyolk (and a slight bit of water) on them. Mix the yolk with the paint using the tip of the brush, then apply it to the artwork. Over time the yolk will ooze out of the yolk sack, that's fine, it's still useable outside of the yolk sack.
The online tutorial is a bit different. It says to pierce the yolk sack and blend the yolk with water, then use the yolk/water mixture with the pigment. I have not tried this, but I'm sure it works just fine.
When you use the yolk straight, it is thick and dries with a slight shine. I would guess that cutting the yolk with water will be thinner with less shine.
Step 6: Color Sample
If you want opaque coverage, you need to use gouache (pronounced goo-ahsh). Gouache is watercolor, but it is designed to go on opaque.
If you are using multiple colors, be sure to have a container of water to rinse your brushes and paper towel to dry them.
Step 7: Drying and Clean Up
To clean your brushes, use some dish soap and water. Don't let the egg dry. If you do the bristles will be ruined.