You can do a global search of all available test results to see if you come up with any matches. If there are any, you can work on trying to piece together what the relationship is with those other genealogists.
Once your results are available, you'll be able to go into your personal page at FTDNA and do a search for yDNA matches. You'll always see all of the other results in your surname - and at that time, you'll be able to select a preference that allows you to compare against all others of all surnames who opt in to the FTDNA internal comparison. (When your results are back, we'll post them on your surname project’s Results page.)
You'll also be able to upload your results to Ysearch (FTDNA's public database - open to all) and see who you match there.
FTDNA will send you automated messages when you have a match (either with only your surname project members or to their internal "opted-in" database) - depending on your selection.http://www.worldfamilies.net/faqs.html#compareresults
Also, both Y-DNA and mtDNA will help you discover your "Deep Ancestry," which tells you which population group your ancestors were a part of 10s of thousands of years ago (the technical term is "haplogroup"). Y-DNA tells you your ancestry of your father's father's father and mtDNA tells your mother's mother's mother's ancestry. If you want information on additional branches, testing relatives (aunts, uncles, cousins) can give you more data.