Nearly every week I have a teenager who is upset by something said or done on facebook. Once a month or so, I have a teen who admits to having upset someone else. School counsellors are inundated with this problem, day in and day out.
It's not surprising this issue comes up so much. Teens are on facebook constantly and communicating with hundreds of people each year. Whether to "like" a post, what to say in comment, how to respond to others, staying on the edge of other peoples' conflict, not offending sensitive others, resisting the urge to feel powerful by cutting someone down - it's hard, tricky work.
On the positive side, at least teens are constantly learning about communication and how people respond and feel. They are getting a lot of practise and perhaps this will set them up well for their communication skills in adulthood.
However, they really do need help in managing these issues. They need specific guidance as to what works and what to do when things go wrong. The best way of doing this - as always with teens - is to be asking them questions. Lectures from parents and teachers (which they switch off from almost immediately) are not the answer. Instead, we need to find out, in a genuinely curious and respectful way, what they were thinking when they said something, how they feel about the conflict, what they think would make them feel better, what the next step would be in resolving the issue, how it could go better the next time, how we can help them act in positive ways and so on.
When teens know that you are interested in their ideas, experiences, thoughts and opinions - they start to open up and the conversations become much more powerful. If they think the conversation is going to be about us telling them what to do and what they have done wrong, they shut down.
Asking questions rather than giving advice is hard because we have become used to thinking that our role as parents, teachers, school counsellors and youth workers is to advise and teach. However my experience has been that it turns out that the best teaching we do comes from asking, and listening.
Best of luck!
PS I have put together a couple of handouts which I use with teens to help have this conversation. One is for the "victim" and one is for the "instigator". I ask them to read through them and use it as a basis for questions I can ask them. It's a way of kick starting conversations that are often very powerful. If you are interested in these, I have just posted them on the "articles for teens only" section in this site - feel free to use them in whatever way helps you relate to your teen/the teens you work with.