Great question! DNA is taken from cells, and from there a process called gel electrophoresis is used to identify individual characteristics of the DNA. This process separates proteins into bands of different molecular weights that can be compared against controlled bands of very specified molecular weight proteins. Every human has slight differences in the proteins in their DNA, and so using this method you can compare the given DNA to other humans until you find a match!
Here’s a link to a short video about DNA fingerprinting:
And here’s a link to a longer and more detailed DNA fingerprinting video that explains the process in more detail: