PCR is one of the most important processes in biology today. It is used in medicine, research, and school biology labs everywhere in the world! The best part, of course, is that the process is actually very simple.
There are few materials involved in the experiment. You need 4 primary things: your target DNA (the gene you want to amplify), a primer (a small piece of DNA that can attach to the target DNA), a DNA polymerase that can operate at a high temperature (a protein that constructs the DNA polymer), and nucleotides with which your DNA polymerase can construct new strands.
You start the reaction by heating your DNA strands to a high temperature so that they split into two single strands. This process is called "melting" the DNA.
You add a large amount of primer DNA molecules and cool the solution, so the primers will attach to the Target DNA. If you do not add very many primer molecules, there is a chance that the Target DNA strands will simply reattach like they were before you started! By adding a lot of primer, you ensure the reaction will proceed as you want it to.
Next, the polymerase takes effect. You heat the solution to the temperature at which your DNA polymerase is most effective, and it will construct the complementary DNA strand from the Target DNA template.
When the process is complete, you end up with twice the number of DNA molecules as you started with (ideally). You can then repeat the process to "amplify" a gene by several factors. For example, if you repeat the process once, you will have 4 times as many DNA molecules. Repeat once again, and you will have 8 times as many. However, remember that these are ideal numbers, and it is much more likely that if you run the experiment in real life, you will have a lower yield, of course!