According to WebMD, a person's skin completely replaces itself every 27 days. HowStuffWorks indicates that skin is made up of about 1.6 trillion skin cells; these cells are continually turning over.
KidsHealth explains that the skin has three layers, and the top layer, the epidermis, is always making new cells. They are formed at the base of the epidermis and gradually move up in the layer. At the same time, old cells die and work their way to the very top, where they are discarded.
Every hour, between 30,000 and 40,000 dead skin cells are sloughed off, HowStuffWorks states. This adds up to about 1 million cells in one day. In a year, over 8 pounds of skin cells are dropped off and replaced.