A huge subject. Cancer is defined as a tissue displaying persistent purposeless proliferation.
It is divided into benign - non invasive and localised - and malignant - invasive and liable to spread to distant sites.
Cancer can fail to show itself until it is too late or show itself in many and variable ways.
Probably the commonest cancers we deal with are growths of the skin and sub-cutis. Pretty well any lump you find is worth checking with the Veterinarian. Diagnosis will probably involve taking a small sample (biopsy, fine needle aspirate, impression smear) or by surgical removal followed by a pathologist opinion in the tissue.
Internal cancers may be more difficult to diagnose and X- Rays, Ultrasound or Surgery will usually be involved in the investigation of such growths.