Handwash the bedding in a large basin with a mild biodegradable soap the first three or four times you care for them, using cold water. Rinse with cold water and air-dry the bedding outside on a clothesline.
Wash the bedding after the initial three or four hand-washings in a machine on delicate with mild biodegradable soap. Use cold water, and do not use the extra spin cycle. Do not wash with any other items. Air-dry the sheets outside on a clothesline.
Iron the sheets when they are still slightly damp with a cool iron, pressing them on the non-shiny side. Use a clean white cotton handkerchief between the silk and the iron to protect the silk fabric from water spatter and marks from the iron.