It is a very simple process, and if you do it without your kids around they will get even more enjoyment out of the whole deal. All you need are some hard boiled eggs and food coloring. Hard boil your eggs any way you prefer. I like to do mine in the oven a al Alton Brown, but traditional boiling works great too. Once your eggs are cooked allow them to cool. Fill up a bowl if water and food coloring. Or use a bunch if smaller cups with lots of colors if you want variety.
You are essentially doing to dye eggs like you have for Easter. However, before placing your eggs into the dye gently crack the shell. You want lots of tiny cracks all over the egg. Try not to take off any huge chunks, but small flakes are okay. Then place your eggs into the dye mixture. Leave them submerged in the refrigerator over night. In the morning you will have beautiful speckled eggs that will convince any kid they are from a real dinosaur.
Even more fun is cracking into them. The whites of the eggs have also been dyed and the cracked pattern shows on them as well. My kids enjoy their eggs over a piece of toast for breakfast. My daughter has also suggested that we use dinosaur eggs the next time I make deviled eggs. I sure this would make quite the conversation starter at any party!