Sometimes you come across an ancestor for whom you can find no background information at all. You may know their descendants, but have no clue or even guess as to their origins. Parents, siblings, and anything about their children just seems to be missing. They are an entity unto themselves, seemingly come out of nowhere, with no background information in sight anywhere. These are frustrating ancestors to research. It can take years of studious, devoted research to dig up even the tiniest bit of information on them, and when you do, it will seem like the biggest genealogical victory in the world.
The invention of DNA testing has made teasing the background out of these mystery ancestors a little bit easier. If you are very intrepid about looking through even the most obscure record sources and have a lot of patience, you can often piece your ancestor's background together using previously unknown records and DNA testing. If you are determined to find out where this mystery ancestor came from (since everyone came from somewhere, whether it is apparent or not), then these are the techniques you should be using to discover things about your ancestor you never dreamed were available.
First of all, use what you know about this ancestor's descendants. Trace their family tree from them down to the present. Then, get in touch with as many descendants from as many branches as you can. There may only be one branch, if your ancestor only had one child, who had one child, etc. But anytime there is more than one child in a generation who grew up and had their own kids, you've got a new branch. The more representatives of each branch you can get to agree to do a DNA test, the better. You can not only prove all of these people share a common ancestor in your mystery ancestor, you can often make matches with other people online who share a common ancestor with you and your testing group.
If you all get the same matches, it usually means your matches are descended from other children of your mystery ancestor's parents… your mystery ancestor's siblings. You can get in touch with them and compare ancestral notes to see if your shared common ancestor has the same last name and came from the same (or close to the same) place as your mystery ancestor. This is your first clue to your mystery ancestor's parent generation.
To confirm it, you need to do a deep record search. If you have looked through all of the available records you can think to look at, start looking at records pertaining to the mystery ancestor's neighbors, as well as records pertaining to their spouse and their spouse's family and neighbors growing up. Land records and wills are particularly useful. People usually did not live in isolation in centuries past. People who lived near each other often had connections to each other. Even if you can't find any records your mystery ancestor left, you may find them mentioned in a land transfer record, a will, or a military pension record for one of their or their spouse's neighbors. That mention will give you a clue, or even tell you outright, how your mystery ancestor is connected to the person who generated the record.
When you put all of the clues together, using both DNA and obscure records generated by people close to your mystery ancestor, you will often be able to put together the story of their life and background. You may even be able to get definite names of one or more parents, which gives you another generation, and a greater chance of taking that line back even farther.
