I haven't done FTDNA yet, but they all pretty much have to work the same way.
There's a centiMorgan (cM) number for each match, and that can be used to estimate how closely-related you are to them. The higher the cM number, the more precisely you can tell the relation.
Beyond that, they undoubtedly tell you what other people you BOTH match. Once you start to figure out how some of your matches are related, you can generally tell which side of your family (thru which grandparent, great-grandparent, etc) the person is related from this list. If it's a relative on my dad's side, my 1st cousins (on my mom's side) are not going to show up on that list.
It's very much like a jigsaw puzzle that way - as you get a number of key pieces in place, the next few become a bit easier, and the next few after that become easier still. When I start on a given site, it's usually a "who the heck ARE these people?" situation, even though I've done extensive research on distant relative. But eventually, I figure out who most of the people above about 50cM are.
With the other sites, if they're notifying you of a specific new match, that probably means that it's a fairly high-value cM, and you have a good chance f figuring out how they're related.
So how many cMs IS this new mystery match?
