Fingerprinting doesn't rely on DNA sequencing, but does rely on the DNA sequence being different between people. Everyone's DNA contains subtle differences (particularly in the non-coding DNA regions). These differences can be exploited by various laboratory techniques to produce small pieces of DNA which will be of different sizes because of these differences. When these fragments of DNA are run down a suitable gel (usually agarose, a substance derived from seaweed) under an electric current the fragments will separate by size. The pattern of fragments formed will be unique for each individual.
Several fingerprinting techniques rely on what most programmers would best recognise as regular expression matching. For example there are enzymes in biology which will recognise certain DNA sequences but not others, and will cut the DNA in two where ever this sequence is matched. (in perl:
my @dna_fragments = split
is the equivalent of what an enzyme called EcoRI does). Not everyone will have the same numbers of this sequence in their DNA, and nor will they be in the same place, thus the number and size of fragments will differ. By using a suitable range of such enzymes you can generate a pattern of DNA fragments which is sufficiently unique as to identify a single person amongst a population of several billion.
for more information take a look at DNA Profiling on wikipedia