To provide less fodder for cyberbullies, educate your children about the importance of maintaining decorum and privacy both online and offline. If there's already a cyberbully harassing your children, you'll also need to teach them how to handle it. The best strategy in many cases is to ignore the bullying, or at least not react to it. While it's not always easy, simply deleting hurtful communications or avoiding dwelling on them can often help diminish the cyberbully's eagerness to continue. You can also consider approaching the parents of cyberbullies (if you know who they are) to see if they're willing to intervene.
If you suspect your kid is the one doing some cyberbullying (teens often switch back and forth between bully and bullied), explain how awful it's probably making his or her victim feel. Also, emphasize how cyberbullying is neither funny nor harmless, and how their negative actions can have serious consequences.