How do a polymerase chain reaction, gel electrophoresis, and restriction enzyme relate to DNA fingerprinting?

polymerase chain reactions basically have an enzyme that cuts out a specific part of the dna code (for instance everywhere CAGCAG is found in the DNA, it is cut on one side).

so, for the one strand of DNA that was cut at the site of CAGCAG, another enzyme will add the complimentary nucleotides. without getting too technical... the cut part of the DNA becomes replicated over and over to get the same piece of DNA.  

Gel Electrophoresis is used to determine the length of a strand of DNA. The heavier (or longer) strands will stay closer to the starting point on the gel, and the smaller dna fragments will travel further.  This is the resulting lines that you will see on the gel.  This is many times how different DNAs are compared (say for instance between a father and son, there will be many DNA fragments at the same points on the gel)

restriction enzymes are used in processes like polymerase chain reactions to splice a piece of DNA off of an entire DNA strand that is many nucleotides long.