Keep them dry. Do not get wet or immerse in water. This will leave a white residue on the clay, and the colour might lighten or become dull. It may also weaken the materials of the earrings.
If this happens or if you get makeup residue on the clay that you'd like to clean (or if you'd like to refresh the colour of the clay), gently apply a little bit of baby oil using a lens wipe, then very carefully wipe away any remaining oil with a piece of clean soft fabric.
Store earrings carefully, out of the heat and away from direct sunlight.
Be gentle when wearing and removing your earrings.