Wash your cast iron cookware by hand. You can use a small amount of soap. If needed, use a pan scrapper for stuck on food. For stubborn stuck on food, simmer a little water for 3-5 minutes, then use the scraper after the pan has cooled.
Dry promptly and thoroughly with a lint-free cloth or paper towel. If you notice a little black residue on your cloth, it's just seasoning and is perfectly normal.
Rub a light layer of cooking oil onto the surface of your cookware. Use a paper towel to wipe the surface until no oil residue remains.