Contrary to popular belief, cupping was not first used in the Olympics on Michael Phelps, but has been in practice for over 2000 years in Traditional Chinese Medicine, as well as in many other Latin and European cultures. Similar to acupuncture it is based on the premise that at any given time we are all suffering with some subjective degree of stagnant blood obstructing our circulation.
The suction from the cups is able to draw said blood out of the muscle layer and up to the surface, thus allowing healthy fluids to move freely. The temporary bruises are not actual "bruises" (nor painful), but are evident of blood coming to the skin. It is a very safe practice when done by professionals, however it is important to not allow cold air to blow on the bruises for a few days afterwards, as the muscles are vulnerable to the constriction created by the cold.
Cups are usually retained for no longer than ten minutes. The quantity of cups used depends on the severity of the patient's condition and strength of their physiological constitution. For example, we are less likely to use ten cups on an 80-year old, conversely less likely to get effective results from only two on a 20-year old.
The traditional format is glass "fire cupping," which works by quickly withdrawing a lit cotton ball held by a hemostat to create a vacuum-like pressure from the glass. Contemporary practice has now offered the plastic suction cups as well, which do not slide up and down the muscles as easily, but are thought to be equally as effective.