The most common method is called "shave removal", which involves numbing the area and using a medical razor to shave the mole without effecting the normal contour of the skin. Another acceptable method involves cutting out the mole and stitching the area closed. Any mole removed should always be studied under a microscope to be sure that it is harmless.
Because the brown color of a mole is caused by melanocytes (a special cell that gives color to the skin), occasionally a mole may return after it has been removed. If this happens, it should be evaluated by a dermatologist. Therefore moles should never be "frozen" or "lasered" off.
There are many other types of skin "spots" that are not moles that can easily be treated without cutting them off. These include freckles or sun spots and brown wart-like growths on the skin. Lastly most moles cause no problems but if there is concern or any sign of change in a mole, it should be evaluated by a dermatologist.