The truth is, Facebook is as private as you would like it to be. You can choose who can view your information, what information you see, and even if someone can find your name when they search the website. One of the best resources I have found that guides you through Facebook is the CIO Facebook Bible. If you want to start out with ten simple steps try their 10 Essential Tips & Tricks for all Facebook Users.
I just learned to clean up all those game requests I keep getting and have no interest in!