Genetic fingerprinting (also called DNA profiling) is the general term applied to a number of processes that provide a limited picture of a person's genotype.
Genetic fingerprinting essentially began thirty years ago with restriction digest, also known as restriction fragment length polymorphism (RFLP), a technique that used a restriction enzyme to chop up a person's DNA into segments at the enzyme's restriction sites. This process made fingerprinting very popular, as it offered a cheap method for applying concrete genetic information to forensics applications and paternity tests. The figure below shows the very basic idea behind RFLP: the lengths of intervals of DNA would be different for individuals having restriction sites at different locations of the genome.
A more advanced technique is to use microsatellites, or "short tandem repeats." These 2-6 bp repeats occur several times in quick succession, with the precise number of times varying between individuals and forming an allele. The figure below contains a DNA profile for 14 different humans; each colored band represents a different microsatellite, with the position of the band indicating just how many times the microsatellite is repeated. Notice that no two individuals have the same set of bands.