21st Century Genealogy
In her case, the name is Gottesman, her GGM. She emailed me because my GGGM was Beila Gottesman from Medyka/Przemysl, as listed in the JewishGen Family Finder. If you have any living Gottesmans in your tree, be sure to visit her site!
There are two main ways to test your DNA. The y-DNA test traces common lineage along an unbroken paternal line. For me, it baselines my Semmel roots--my father's, father's, father's, etc... It can tell if I am related to other Semmels (or Semels, Zemels, etc...) It also reveals much about ultimate origins -- Cohanim? Levite?
There is also a maternal line test using M-DNA. Because of name changes, it seems less useful for recent generations, but does yield fascinating deep roots information as scientists have narrowed down most of humanity as having sprung from one of 7 "Daughters of Eve" Unlike Y tests, this one works for males and females. (though all your M-DNA comes from mom!)
The test itself costs around $1-200, depending on how many markers you want to establish. In general, more markers means more accurate results. No blood - it's all done from a swab of your cheek.
I just ordered a Y test kit. I'll post the results when I receive them!