- You buy some primers which are basically chunks of nucleic acid that match whatever gene you want to look at.
- You put DNA you've extracted together with these primers into the PCR machine. This makes lots of copies of the gene you're interested in.
- Then you put the resultant amplified DNA into an electrophoresis gel box (such as the one sold by http://www.pearlbiotech.com/ who also provide free plans. This is also run by Tito Jankowski of the OpenPCR project) which lets you look at the actual genotype (you compare the striations from your sample against other samples or a reference).
Primers are cheap and easy to get hold of and as other comments mentioned there are various software tools for letting you design them (you then place an order with a company like Invitrogen).
Edited to add:
The reason you need to amplify stuff is because biology is annoying like that. Let's use a simile:
If particle physics is figuring out how a watch works by smashing it against a wall and studying the debris
Then biotech is throwing gears and springs into a test tube and carefully stirring at certain temperatures until you can hear ticking.