Since everyone creating a Facebook account is (more or less) required and expected to use their real name, and a verified email address, you can search for your friends by typing their name or email address into Facebook’s search field.
Facebook’s Find Your Friends tool gives you many other options, such as entering your account name and password from various other services (like Gmail, Yahoo, AIM, MSN), thereby giving Facebook permission to search your address book for people who already have their own Facebook account.
Maybe the most natural thing to do is look at your existing Facebook friends and see whom they are friends with. (For example, you could look at my assorted friends.)
Using any of these methods, you can select those folks you both know and like, then ask them to be your friend.
