First, shave in the direction of the hair growth.

Second, never "rub" dry or "rub" clean those areas, simply pat it dry and pat it clean.  It works!!!

Reason being is your folicles will swell where the skin is sensitive due to razor irritation, if you cut the hair against it's growth direction the hair will more than likely receed below the surface of the skin and become ingrown due to the irritation.  Rubbing to cleans or dry the skin after or during shaving aids in irritating the skin.

A girlfriend taught me this once.  The ladies have all kinds of little tricks when it comes to personal hygene.