Whenever someone I know becomes a Facebook friend, I send them a link to an article that is available (just Google it) called “5 Easy Steps to Stay Safe (and Private!) on Facebook” (I know the mods will not let this through with a link in it). It’s absolute must reading for everyone, adults, teens etc.
One of the most overlooked features of FB is privacy settings. What I’ve done is create lists of friends by categories such as people from my kehillah, other friends, relatives, work associates, etc. Then you can use those lists as easy ways to filter what you post. For instance, perhaps I don’t want my work associates to see my pictures. So they’re in an album filtered to either allow or block specific group(s). Or, on the otherhand, if it’s very generic, you can omit filters. It’s worth spending the time to review the settings. The idea being that FB should allow you to share stuff with people, but allow you the ability to limit how much and with whom you want to share anything. That doesn’t only mean pictures, but virtually anything about you that you post, be it education, work history, status updates, etc. You can also utilize the privacy setting to set how people can locate you. For example, if they know your email address, can they find you via a search?
Bottom line is use common sense. You wouldn’t tell a casual acquaintance something very personal, would you? The same applies here. And don’t accept a friend request unless you know who the person is! Just like you don’t let strangers into your home.