With the DNA test, it's spit in a tube and send it off. Ancestry is the biggest database and you can download your DNA file from there and upload to other sites such as MyHeritage and GEDmatch but you can't upload a DNA file from another company to Ancestry.
When it comes back, you have your ethnicity details which isn't all that reliable and for me, not that interesting albeit it's why a lot of people do the tests.
What you also get is a list of people you share DNA with and the amount of DNA you share with them. The higher the amount of centimorgans, generally, the closer you are related. There's a "DNA Green Chart" which is a good headstart to giving a suggestion as to how far back the Most Recent Common Ancestor between you is.
If your tree is comprehensive and the details of people in your tree match those of someone you share DNA with, you get a "shared ancestor hint" which basically identifies the Most Recent Common Ancestor between you. However, given computers are essentially stupid, if there's a slight different in the details, it won't consider them the same person.
Most of your matches won't have a Shared Ancestor Hint for and what you need to do then is compare your tree to their tree to see if you can work out the MRCA. There's various tools to help you do this although they all rely on the other person having a public tree;
1) he computer will identify shared surnames in both of your direct ancestors
2) you can view a map of the birth locations of people in their tree so if you have a very location centred tree (I do - my family are from Lye and Cradley for hundreds of years) I can look at which of their ancestors are from this location and that gives me a head start in who i'm looking for in my tree
3) it will also tell you the people who share DNA with both of you
It's a whole new ball game of research
But it doesn't lie ... trees and paperwork can be wrong but the DNA isn't.
In your case, if the daughter took a DNA test you would hopefully be able to find some close relatives who could unlock that surname for you by their trees, or pick up on a surname that keeps cropping up in other trees that you can research.
If you're on facebook, I can recommend you joining a few groups such as AncestryDNA Matching and just watching. It will all seem like goobledegook to begin with but you'll very quickly get your head around it.
That's just a very brief introduction into what you can do with DNA. There's a whole load more really neat things you can do but best to get your head round that first.
Also, Black Friday is coming up and there will undoubtedly be some really good deals on.