The how-to pictured is for the ladybug egg, but this simple technique can be applied to any creation.
Start with an egg dyed a pale color. Press a finger into a stamp pad containing non-toxic, water-based ink, then press onto the eggshell to make polka dots, little creatures, flower petals, or other desired patterns, redipping in ink as needed. Set eggs on a pin-board to dry, and wash hands.
If desired, use a fine-tipped permanent marker to add details such as beaks, legs, antennae, and flower stamen.