I already had some beets, coffee grinds and turmeric in my kitchen so I went with those. I made the base from a recipe I found in Yankee Magazine: Combine 4 cups water, 1 tablespoon white vinegar and 1 tablespoon salt.
To make the Red Coloring I added chopped beets to my base mixture, brought it to a boil and then reduced the heat to a simmer for 30 minutes, until the liquid had a deep red color to it. I strained the beets out and let the liquid cool down.
For the Yellow Coloring I added 5 tablespoons of turmeric spice to the base liquid, mixed it well and let it simmer for a few minutes until the spice was thoroughly dissolved. Then poured it into a bowl to let cool.
Brown Coloring required 4 tablespoons of coffee grinds mixed with the base and brought to a boil, then simmered for 10 minutes or so. Strained into a bowl and let cool.
Once I had poured all the liquid into different containers, I let the eggs sit overnight for about 7-8 hours, though 3-4 hours would be plenty if you don't have time to leave them overnight. Just make sure the liquid completely covers the eggs.
And that was it. Fairly easy and simple process for nice, naturally colored eggs. Happy Easter!