You make the process sound a lot simpler than it is! While it is fairly easy to conduct PCR, you need to find the right primers
(bits of DNA to get the process started), and you'll need the chemicals and a thermocycler. Do you have access to these materials at your school? Try doing an internet search for "PCR protocol," which will give you access to many online protocols. Here is one: http://www.mcdb.lsa.umich.edu/labs/madd ... tocol.html
When you do PCR, you do not usually copy the entire genome. You pick your primers to target a specific area of the DNA to copy (which should contain your gene of interest). Humans have 23 pairs of chromosomes, and it is not yet known which gene or genes are responsible for alopecia areata. There are several candidate genes, including the ULBP3 gene, but we do not yet know the exact cause of the disease. Here is a scientific article that found several candidate genes for alopecia areata: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1785354/
Once you do PCR, performing sequencing of the DNA is a much more complicated (and usually expensive) process, especially without the help of a research lab. I do not want to discourage you, but if you are working with limited resources and time, I do not think that gene sequencing is the way to go.
One way to examine the heredity of a trait is to construct a pedigree
. This would require the full participation of family members, but you could try to see whether your condition has shown up anywhere else in your family tree, which would support the idea that it is inherited. Check out this Science Buddies project to help you get started with the idea of pedigrees: http://www.sciencebuddies.org/science-f ... ml#summary
Let me know if this sounds interesting to you, or if you want to try another option. We will find something that works for you!