The following are widely considered to be the better sources of information and kits on DNA testing for genealogical research:
- AncestryDNA (http://dna.ancestry.com/?s_kwcid=ancestrydna&o_xid=58712&o_lid=58712&o_sch=Paid+Search+%E2%80%93+Brand)
- 23andMe (https://www.23andme.com/)
- Family Tree DNA (https://www.familytreedna.com/)
If you are interested in getting more information about how this works and why it has become so popular, MIT published an article. You can find it at: http://www.technologyreview.com/news/405384/tracing-your-ancestry/
On 19 Nov 2014, the Ancestry.com blog did a post about improvements in DNA matching that you might find interesting.
A Google search will produce hundreds of links to useful information.