Facebook got rid of the refine search. So now unless you know someone's full name (as they spell it on Facebook) can you find them? For example I know someone's first name and information about her (such as she lives in the same city as me), but without a last name I can't seem to even get anywhere close.
People named "Mark" who live in San Francisco, California
If you don’t see the person you’re looking for, don’t despair; you can get more results:
Type the person's full name in the search box.
Click See More at the bottom of the search menu.
The search menu expands to reveal new options for search. So, if you type Jane Smith and then click See More, you can now either search People Named Jane Smith, Pages Named Jane Smith, or Places Named Jane Smith.
Click the People Named option.
A blue friend icon is next to this option. A search results page appears with larger previews of people’s profile pictures and Timeline info. The right side of the page also has options for narrowing your search using fields such as Gender, Employer, Current City, and so on.
Use the fields on the right side of the page to zero in on your actual friend.
This might be information like where your friend works or where she's from.
When you find the person you’re looking for, add her as a friend.