Hi Springrain, hopefully their explanation will help:
https://www.facebook.com/DNADoeProj...009255824516/2029919493933492/?type=3&theater
Basically their team of genealogy volunteers goes to work after all the DNA science-y stuff has been done, and using GEDMatch, which is a database that the Doe DNA was uploaded into (similar to but much smaller than Ancestry or 23andme) starts painstakingly constructing the family tree. It's apparently really complicated and there are tons and tons of names to work through. With a lot of hard work and luck they may come up with the Doe's name after working on their family tree. How long it takes depends on a lot of factors, like how degraded the DNA was, how represented their background is in the database, etc. It can take a surprisingly short time or months and months. Does that are black, latino or Native American will probably be much harder to identify because their group is underrepresented in an already small database so there aren't as many distant or close relatives to work with. If you email them or reach out on Facebook I'm sure they'll have a much better explanation but this is how I understand the very basic gist of things in layman's terms
Anyone can upload their DNA results from 23andme or Ancestry, etc. into GEDMatch to indirectly potentially help solve Doe cases and help adoptees find their birth families. It's a cool database that allows this kind of work.