DNA fingerprinting works by extracting DNA from a sample, cutting the DNA into fragments of varying lengths using restriction enzymes, sorting the fragments by size through gel electrophoresis, transferring the fragments to a nylon membrane, exposing the membrane to radioactive probes that bind to fragments of matching DNA composition, and developing photographic film to view the unique pattern of dark bands that make up an individual's DNA fingerprint. This process allows law enforcement to compare fingerprints from crime scenes to those of suspects.