Facebook allows you to connect with anybody you want -- but it also offers you options to limit access to your personal information for those you don't know or trust. Namely, Facebook provides you the option to display a limited profile to certain users.
Typically, your Facebook profile shows your photos and wall posts, information about your work and education, and a list of your interests, hobbies and activities. When you configure your limited profile, you can choose which of these you do and don't want users you designate as being "limited" to see. For example, you might block access to your contact information or your list of employers and schools to people who don't know you very well.
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How to Limit Access
Facebook allows you to limit access when you befriend someone. When you add someone as a friend -- or, if he adds you, when you accept his request -- click "Add to List" and select "Limited Profile" to limit him. Doing so will allow your friend to access only your limited profile. You can change this at a later date using the "Privacy" menu under the "Account" menu at the top of your Facebook page.
Facebook users you designate as being limited don't receive any notification that they're only able to view your limited profile -- and they won't be able to find any indication of this by browsing your Facebook page, so you won't have to worry about them being offended. The only way a Facebook user can know she's viewing a limited profile is if she views your profile through the account of someone who isn't limited or, obviously, if you tell her.
The Facebook "Chat" box appears at the bottom of the Facebook window and enables you to chat with other users in real time. It's also possible to make use of your limited profile here. Namely, you can configure Facebook Chat such that users who can see only your limited profile don't appear in your list of online friends -- even if they're online -- and you won't appear in theirs. Click "Limited Profile" under the "Friend Lists" tab within the Chat box and then click the green and white bar next to "Limited Profile" to "Go Offline" to friends designated as being limited.