Sequence analysis
The basic idea is to look at certain loci (places) in the genome which are highly variable between people. About 10 to 15 of these loci are needed for a match, and the legal details differ between countries. A match between a sample and a suspect individual makes it extremely likely that the individual was the source of the sample. This evidence would then be the basis of the prosecution case for a crime. A similar analysis would show that a man was very likely the father of a child. This is really a modern way to do what was done with blood groups before DNA details could be analysed. The methods have been developed mainly by the work of Alec Jeffreys.