Trust your child but verify what is happening. Tell them "I trust you. If something does happen I am here to help you."
Make sure the computer is centrally located in your house so that you can monitor what is happening. And while you know what they are doing at your house, what are they doing when they are visiting a friend's house?
Educate yourself on what they are doing--learn the technology they are using. Set up a Facebook account and learn to tweet if they are using these technologies. Use netlingo.com if you don't understand what they are saying.
Of course, educate them to NEVER put their first or last name as email address. Don't tell people online where you are from. Don't tell them your school. Don't send out photos of yourself to people you don't know. Don't ever respond to a request to meet in person. Don't respond to unsolicited email asking you for account information. Don't post plans like where you will be on sites.
LET THEM KNOW:
SAVE everything. If they get a mean email or a compromising picture. They should SAVE the email. There is a tendency to destroy it but a compromising picture or mean email is evidence and they will not get in trouble IF they tell their parents and their parents tell the authorities. This is not for the purpose of prosecution. They want to stop these kinds of emails from being forwarded. Tell them they should not forward the picture/email to ANYONE because you/they can be charged with trafficking indecent material of a minor if you continue to forward. They should call authorities. While these things might seem minor their have been instances of kids killing themselves because of pictures/posts/emails and it is not something to take lightly.
Facebook, the company, recommends that teens be 16 to get a Facebook account. If your kids do use Facebook, DEMAND that you set up the account for them AND make sure you have your own account and you are friends with them so you can view content. Don't add people to your friends list that you don't know. More information can be found at GetNetWise.org Facebook Privacy Information.
If you want to have the District Attorney's Office come speak to a group of parents or a separate group of children (usually 6th grade and above) about internet safety or cyber bullying you can find the number of the Office of Community Affairs at the District Attorney's Office and have the school or PTA contact them to make arrangements. In New York City, the number is (212)864-7884 to arrange for this kind of presentation.
Here are some links they mentioned with more information: