You do not need to clean your breast or nipple in a special way before or after feeding your baby. Rinsing your breast with plain water while having your daily bath or shower is all that is needed. Avoid anything that dries out or otherwise damages the skin. This includes the use of soap or disinfectants on the nipple and areola as this can dry your skin and may contribute to sore nipples.
Already during pregnancy the Montgomery glands surrounding the nipple start to secrete a natural oil that lubricates the skin and discourages the growth of bacteria. It is perfect to leave this natural substance do its job.
You may express a few drops of milk after feeding, massage it gently into the skin and let it air dry. If your skin is especially dry or damaged you may apply a tiny amount of modified lanolin (e.g. PureLan) to your nipple and areola. Bras and bra pads should allow the circulation of air. Any kind of plastic lining in bra pads or bras should be avoided.
Breastfeeding is not meant to hurt. If you experience nipple pain or soreness ask your lactation specialist.
