Like any other social interaction (online or in person), Facebook is what you make of it.
Each individual user can set his or her settings to allow certain levels of disclosure for different levels of users. For example, your daughter could set it so only approved friends can see her pictures, read or write on her “wall” (a page on her profile kind of like her own personal message board visible to others), and see what school she attends. She could set up a special group for “friends” that she doesn’t want seeing certain details of her life. For example, she could set up a group for “teachers” that she wants to connect with, but doesn’t want to be able to read her wall (in case she comments “mr johnson is sooo boring!”)
Facebook isn’t really conducive to chatting in groups, and certainly not with strangers. It could be used that way, but it’s not set up to facilitate that.
I suggest you sit down with her when she registers and help her go through the different levels of Privacy Settings, talking in detail about WHY you think certain information should be private. Speculate on the possible negative effects of sharing too much information with too many people. Go beyond the “there could be creeps out there” topic, and cover other reasons to guard one’s own privacy.
For example, you could set up a friends group called “Close Friends.” “Photos and Videos of Me” should be visible only to those Close Friends. The reason: Over time, she will accumulate many Facebook “friends” including teachers, grandparents, or friendships that dwindle. A picture of her, uploaded by someone else and “tagged” with her name, might be embarrassing in some way (an unflattering angle, a silly pose with friends that grandma just wouldn’t understand, etc.) Then she can add people to (and remove people from!) the Close Friends group as time goes on.
That’s just one example. Having been a teenage girl on the internet when the internet was still “new” (I was online as early as 12, back in 1996), I wish I had been more thoughtful before posting personal things online. For example, my crush found out I liked him when he found a picture I had drawn of him on my personal website (which resulted in a LOT of teasing).