The basic process remains the same in each type of cancer - cells divide in an uncontrolled fashion, destroy the surrounding healthy tissue, migrate through the blood into other parts of the body and proliferate further as secondary tumors (metastases).
Cell division occurs also in the healthy organism. Cells in the human body have certain backup systems that guard against unrestrained cell proliferation and see to it that a cell only proliferates when it is necessary for the body, e.g. in the new formation of blood, in healing wounds, and in growing hair. Cancer cells have lost a number of those backup systems due to mutations in the DNA.
One such backup system is a mechanism called programmed cell death (apoptosis), a complicated sequence of events through which a cell commits suicide. These events are initiated in response to mutations in a cell's genetic material or other signs of an abnormality. Cancer cells do not respond to signals triggering the apoptosis program; in fact, an important step in becoming a cancer cell is gaining the ability to evade the programmed cell death.