There are a few different companies that do DNA testing for genealogy. I have written before about my experience using AncestryDNA, first at AncestryDNA - One Jewish Result, then at AncestryDNA Updates Ethnicity Results ~ Jewish Results. AncestryDNA does autosomal testing, which means it is a test that provides a breakdown of one's ethnic percentages, to find out where all your ancestors may have come from going back hundreds of years. However, you don't know which ancestors (maternal or paternal or your mother's grandfather) these ethnic percentages apply to.
Family Tree DNA is another testing company which does Y-DNA testing and mtDNA testing, in addition to autosomal DNA testing.
Y-DNA testing, which only men can take, traces a man's father's father's father's line, which can be used for surname studies for men trying to confirm if they descend from the same man (assuming the surname has remained the same over the years). This doesn't really apply to Jewish genealogy, as surnames do not apply for enough generations to go back very far.
Then mtDNA (maternal) testing, which traces a person's (either male or female) maternal ancestors (mother's mother's mother, etc.), lets that person know what his or her maternal origins are 20,000 to 100,000 years ago.
Awhile ago, I had my husband take the Y-DNA test (at 37 markers), and the results show that his haplogroup is R-M198, also known as R1a1a. According to my notes from Bennett Greenspan's talk at the IAJGS Conference in August, this Haplogroup goes back to Eastern Europe or Western Asia. Half of Levites are in this Haplogroup, so the story that has been passed down orally in my husband's father's family that they are Levites is supported by this testing result. It has been suggested (via Wikipedia) that the R1a1 Haplogroup originated about 21,000 years ago in southern Russia. This Haplogroup is most often associated with Russians, Hungarians, Poles, Ukrainians and Belarusians (also Wikipedia).
Below is a screenshot of the map that shows where the R Haplogroup split and then where R1a ended up - in Eastern Europe.
My husband's grandfather, Joseph Handler (1884-1947) was born in Ilok, formerly in Hungary, then Yugoslavia, now in Croatia. I know nothing more about his father than his name was Aaron (or Adolf, or Arthur), that he was believed to have been born in Yugoslavia (based on that notation on the death certificates of his sons, Joseph and Sam), and that his Y-DNA was the same as my husband's.
For better explanations of genetic genealogy, visit Your Genetic Genealogist blog, written by CeCe Moore. She also wrote an article for Geni.com explaining Y-DNA testing, where she explains it much better than I ever could.