There are only four genetic "races": Indo-European, African, Native American, and East Asian. Many people have a mixture, to some degree or another. If you are of mostly European ancestry, and had a gggg grandmother that was Native American, you might show up as 5% Native American, and 95% Indo-European. Some people have a few different racial ancestries.

I paid a genetics company to have my genes scientifically tested and it was found that I am 100% Indo-European. This test covers six or so generations back - which involves quite a few ancestors. To get a DNA sample, you scrape the inside of your cheek with a plastic thingy, put it in a container with liquid that they provide, and send it in to be analyzed.

I had a few other DNA tests done, including straight male line, Y-DNA, that traces your paternal DNA back many thousands of years. I also had the mT-DNA test, for the maternal line - and that one went back some 18,000 years ago to the Austria/Nothern Italy area. My earliest straight-line female ancester, though, came to the U.S. from England in the 17th century. Her ancestors probably migrated to the British Isles thousands of years ago.