One out of 4 Americans will develop at some point in their lives. Cancerous cells are cells which grow without control. In order to understand how the uncontrolled growth of cancerous cells, we should briefly mention how normal cells control their growth.
Cell division is certainly not a random process; it is very closely controlled.
Every cell has a distinct rate of reproduction: epidermal cells (in the outer layer of your skin) may divide once a day, fibroblasts (in the dermis of your skin for example) only after an injury, and cardiac muscle and nervous tissue cells may never divide in adults. How is this control exerted? This will vary with each cell type but this is a general picture:
a) A growth factor reaches the cell from the blood or from neighboring cells.

growth factor
There are a large variety of growth factors in the body: such as nerve growth factor (NGF), epidermal growth factor (EGF), fibroblast growth factor (FGF), and platelet-derived growth factor (PDGF).

B) The growth factor binds to a receptor on the surface of the cell membrane.
growth factor receptor
There are a large number of cell membrane receptors which respond to growth-promoting signals such as the receptor tyrosine kinases and the G-protein coupled receptors.
C) The receptor activates a signaling molecule inside the cell, typically a protein kinase.

Protein kinases are enzymes which put a phosphate group onto other proteins. The presence/absence of this phosphate group determines whether this protein are "on" or "off". The action of kinases activates many proteins which had been inactivated and inactivates some proteins which had been activated.
c) The Response of the Genes in the Nucleus
Some of the kinases make their way into the nucleus where they change the genes which are activated there (in complex organisms, genes are "off" until they are turned "on" by certain signals). These genes (such as the genes myc, myb, fos, and jun) then direct the cell to divide.
growth promoting genes
D) Preventing Improper Growth
There are proteins (called tumor suppressor proteins) which prevent cell division. There are proteins which can cause programmed cell death (apoptosis) under certain conditions, such as when mutations have caused improper growth. If a cell begins to divide without control, there are immune cells (T lymphocytes) that can recognize and destroy it.

The steps described above are the normal controls over cell division exerted by proteins inside and outside the cell. After a mutation, a cell may produce abnormal proteins which lead to abnormal growth. For example, mutations may cause too much growth factor to be produced. Mutations can produce receptors which always act as if they have bound a growth factor, even when they haven't. Mutations can produce internal signaling proteins (kinases) which are constantly promoting growth, even when they have not been stimulated by a receptor. Mutations can result in nuclear genes which are always promoting cellular growth, even when they have not been activated by the kinases or other appropriate signals. Mutations can inactivate some of the cell's own defenses such as those proteins which prevent cell division or those which cause the destruction of cancerous cells.
Mutations can change the proto-oncogenes (those genes which produce the proteins for normal control of cell division) into oncogenes (mutated genes which result in uncontrolled cell growth). Since there is such a variety of proto-oncogenes in different human cell types, there is a great variety of possible mutations and thus a great variety of different kinds of cancer.
The following cells are in the process of dividing. Are they dividing appropriately or is this uncontrolled growth?
dividing cells dividing cells

Cancer is not one disease: something can go wrong with any one of these steps in any one of the 75 trillion cells in the body. If cells begin to grow without proper control, they are potentially cancerous. What causes the mutations which convert proto-oncogenes into oncogenes?
1) Natural Mutations:
Every time a cell divides, it must replicate its DNA. Every time a cell replicates its DNA, there is a chance that a mistake occurs. A mutation may occur in any part of the genome including a proto-oncogene. The cells which reproduce most often (those of the skin, colon, breast, blood) are most susceptible to this type of cancer.
2) Induced Mutations:
Mutations are more frequent in the presence of phenomena that disrupt DNA such as radiation (X-rays, UV radiation, gamma radiation released at nuclear sites) and chemical mutagens that cause incorrect base pairing by a number of methods:
a) A mutagen may convert one DNA bases to another base with different pair-binding. Formaldehyde and nitrous acid function this way; nitrous acid changes the DNA base cytosine (which binds the base guanine) to uracil (which binds adenine).
b) Some mutagens resemble DNA bases and are accidentally inserted into chromosomes during DNA replication. They cause mutations when they subsequently bind to a nonappropriate base during DNA replication.
c) Some mutagens cause breaks in chromosomes which separate genes from the DNA sequences which control the normal expression of these genes.
3) Viruses:
Some viruses insert themselves into the control elements of a proto-oncogene, disrupting it. They may also mistakenly attach a human gene to the viral genes during the packaging of new viruses: if this gene is a proto-oncogene without its control elements, the gene will signal uncontrolled growth in the next infected cell.
4) Inheritance:
A mutated gene can be passed from one generation to the next which can affect a person's predisposition to developing cancer. As a result, a certain type of cancer may be much more common in one family than in the general population. Since cancer usually involves multiple mutations (e.g. neither myc nor ras oncogenes may cause cancer alone but together they do), inheriting one mutation does not ensure that one will develop cancer, it merely increase the likelihood of cancer.

The following two images are of tumor cells in a patient with had breast cancer.
Below is an image of a normal blood smear. Red blood cells (the light pinkish cells) usually compose 99% of the cells found in blood. The white blood cells (which is stained purple below) represent a minority of the circulating blood cells.

In leukemia, the bone marrow cells which produce white blood cells divide in an uncontrolled manner, producing a much greater number of circulating white blood cells than normal.
leukemia leukemia