Leather/Suede Earrings: Hang them up or store them flat. Keep them away from water, makeup, and hair products. A slightly damp Magic Eraser is usually sufficient enough to clean most trouble spots. If an earring gets bent, cover with a slightly damp towel and flatten with a barely warm iron (avoiding the hooks).
Clay Earrings: While polymer clay isn't as fragile as some other materials, it's still recommended to be handled with care. Do not let clay get wet. If it does, just dab it dry. Do not put or store it with heavy things on top of the clay. When traveling, store in a small box. If you don't have that, make sure that it travels laying flat. Store in your jewelry box where it can't get tangled with other jewelry, or have it hang.