Facebook is a great way to communicate with people and advertise, but there are a few things you can do with your privacy settings to help keep your personal life separate from your students/school related business.
1. You can create a group and/or fan page which allows you to communicate with group members without necessarily being "friends" with them. When they join your group, you can send them messages and updates, event invitations, and upload pictures/video, but they cannot necessarily see your personal profile, pictures, etc if your profile is set as private.
2. If you are going to accept friend requests from students/parents, you can make certain parts of your profile invisible to them, changing the privacy settings so they cannot see certain things. For instance, my students and parents cannot see what my friends post to my "wall," they cannot see my personal pictures, my status updates, comments I make, etc. This is especially important with kids and teenagers. Some people like to use their status updates to communicate with others, in this case you just have to be careful what you post and remember that everyone can see it.
The easiest way to do this is to create a "list" in facebook with certain privacy settings. I have one called "kids" for instance. Anytime a kid/teen requests to be my friend on facebook, I add them to the list, and all of the privacy settings are automatically assigned to them.
If you are not too familiar with facebook, I would recommend sitting down with someone who is and having them walk you through all the privacy settings. It may take a half hour but it is well worth it!