We all have our own DNA, an unique mix that we got from our parents, that they got from their parents and so on...
This kind of DNA is called autosomal DNA and you can use it to try to find other relatives around the world.
Many Americans do have European ancestry and vice versa most Europeans do have American relatives.
In Sweden we are now starting to use DNA to find unknown, living relatives in USA. The way to do this is to use your own DNA as bait and then go fishing in the genetic pool!
And when you got someone "on the hook", a genetic match, you have a really good chance to find out in what way you are related since autosomal DNA dont go very deep. It is most useful for matching someone that have an shared ancestor within 5-6 generations.
This kind of DNA-testing is of course also useful for people that have been adopted or for other reasons dont have much knowledge about their ancestors, but if possible try to also have a traditional ancestral research ready to use when analyzing your results from the DNA-test.
A tip is to test all of your siblings to get a more powerful "bait" when fishing for relatives! You and your siblings most often get some DNA from your parents that you dont share with each other, due to random inheritance and recombination, and that is why you can get matches that your siblings dont match and vice versa. So its not a waste to let all family members take the Family Finder test, but of course its an economical matter since every test do cost money.
As an example, my mother and her brother share about 2740 cM of DNA, which indicates that they have most of their DNA shared with each other (identical twins share about 3380 cM).
Most of their matches are the same, but both my mother and her brother do have several matches that they dont share with each other. In this case, its most likely that my mothers brother got more DNA from his fathers mother and my mother got more from her fathers father.
I know this since I could confirm and assign a match to my mother ( a third cousin once removed) that was linked on her fathers fathers lineage. My uncle however did not have this match at all present in his DNA.
So please join the party, start using your DNA as a bait to find other relatives. I can assure you that this is fun, interesting and very exciting!