Begin with a white, brown, or dyed egg. Tear off a piece of natural sponge. Dip the sponge into watered-down acrylic paint, and dab the egg randomly. Start with light shades and layer on darker colors as desired. Set egg on pin-board to dry.
White, brown, or dyed egg
Egg drying pin-board
Look for natural sponges where cosmetics are sold or at art-supply stores.