Facebook introduced a feature in late 2010 called Friendship Pages that lets you view mutual friends, common pictures and wall posts made between two users. The feature is largely intended to show common friends, photos and interactions between yourself and another user, but it can also be used to view the same information between two different people. This is useful if you are trying to find someone who you know is friends with two of your own friends, because it greatly narrows the search.
Log in to your Facebook account.
Navigate to the first person's Facebook profile and copy their user name or Facebook user ID from the address bar. If the user has a configured user name, you will need to copy everything after "facebook.com/." If the user does not have a configured user name, you will need to copy everything after "facebook.com/profile.php?id=."
Navigate to the second person's Facebook profile and modify the URL in the address bar to read "http://www.facebook.com/[Person 1 user name or ID]?and=[Person 2 user name or ID]" replacing "[Person 1 user name or ID]" and "[Person 2 user name or ID]" with the appropriate information. Press "Enter" to navigate to the Friendship Page when you have updated the URL.
View mutual friends between these two people in the left-hand sidebar.