What drives a cell into uncontrolled growth? Figuratively, as you drive your cell down the highway of life, you have several factors controlling that journey. You have an accelerator to speed up proliferation. You have brakes to stop growth forward. You have fuel in the tank to keep going. Thus, you can have:
Gene activation: accelerated cell proliferation
Loss of tumor suppression: loss of the brakes on cell growth
Persistence: accumulation of cells from lack of apoptosis
Replication: acquisition of the ability to keep dividing
When you have activation of an oncogene, the accelerator can be stuck open. Oncogenes may be genes that were part of embryonic proliferation, but were shut off long ago. They may be genes that normally have some point of control over the rate of cell proliferation, as in epithelium. Acceleration may come from mutation leading to abnormal function of the gene, extra copies of the gene, r amplification of the activity of the gene, or chromosomal translocation that brings two genes together ("fusion gene") that together abnormally produce a proliferative product.
Tumor suppressor genes act as brakes associated with cell cycle regulation, and many of them act at control points to prevent cell division if it is not appropriate. Mutations in these genes allow cell proliferation to continue when it should not.
Apoptotic mechanisms also serve as brakes on growth. There are cell receptors that, when contacting a ligand such as a hormone, will signal the cell to self-destruct. There are genes encoding proteins that oppose this process (anti-apoptotic proteins). Thus, if you turn off the apoptotic genes, or turn on the anti-apoptotic genes, then cells will continue to accumulate, sort of like having all of your friends and relatives come to your house, but never leave.
What about the fuel? One of the most important cellular resources is DNA. In order to keep dividing, cells need to maintain their chromosomes. However, the ends of chromosomes tend to "wear down" with repeated divisions. The enzyme telomerase can maintain the ends of chromosomes. Ordinarily, only human stem cells have active telomerase. Cancer cells often acquire telomerase activity, which makes them "immortal" because they continue cell division indefinitely. Neoplastic cells also need local resources to continue growth, in the form of structural support and blood supply. Thus, neoplastic cells secrete factors that induce growth of connective tissue and blood vessels which support continued growth of the neoplasm.