Draw pictures or designs with wax crayon. Even white wax crayon
will be useful for this project.
Dip in dye.
Let dry.
The dye won't soak through the crayon! I find cheap crayons work
best for this project (crayolas don't have quite enough wax in them
though they do work ok).
An adult may need to help hold the egg while the child draws their
pictures on it... at least the first time until they get the hang of
it.