Follow the directions on the temporary tattoos, and keep the sponge or wash cloth on for the full time recommended!
You just have to make sure that when you put the tattoo on, you don't move until you're ready to take it off (which is much trickier on a smooth egg as compared to a human body!) or else it will smudge.
Thank you Krafts & Kiddos for the fun idea! I'm linking up to Best Mom Advice.