Depends on the protocol and what kind of sample you have.
Skin/flesh/bone take longer because extracting the DNA takes time (couple hours plus, probably overnight). If you have a blood sample, much quicker. If you have to amplify the DNA, that adds a couple hours.
RFLP (restriction fragment length polymorphisim, you use a enzyme to cut up the DNA into fragments, then a radioactive marker that will bind specifically to certain fragments is applied) is more accurate, but takes a long time to run (up to weeks). The advantage is that it is more accurate, I think the chances of 2 samples being the same are less than 1 in 10000.
PCR (polymerase chain reaction, you "cut" the DNA into smaller strands then heat and cool to create more strands then run through a gel that will sort the DNA strands based on length) is much quicker and can be done in a couple hours, but since there are only a few variations that you can look at (you use restriction enzymes that "cut" the DNA when they see a specific pattern), the chances of samples being the same are relatively higher. You run it several times using different enzymes to get a probability that 2 samples are the same but unique from other samples.
I do genotyping on mice and it takes about 18hrs from start to finish. Isolate DNA from the tail clippings takes overnight, prep for PCR 1hr, PCR 3hr, prep for gel 1hr, running the gel 30min.
