First, check the manufacturer's label to make sure that the comforter is made of cotton. According to House Guides at SF Gate, the same laundering methods can be used if the fibers are all cotton or a cotton and synthetic blend.
If the comforter is only lightly soiled, place it in the washing machine along with laundry detergent, and set the machine on the gentle cycle. Fill the machine with cold or warm water, according to House Guides. Gentle washing in the coldest water setting that will remove soil preserves the colors of the comforter and its fabric for a long useful life.
Do not overcrowd the washing machine with other items, since that restricts free movement of the comforter and limits the ability of the washer to clean effectively on the gentle cycle. If the comforter is stained, spray a stain removal product on the stain, following the manufacturer's directions, before laundering. If the comforter is badly stained or it is heavily soiled, pretreat the stain, and presoak the comforter in warm soapy water. After presoaking, launder the comforter on the gentle cycle with an oxygen bleach. Check the label to make sure oxygen bleach is safe for the fabric.