Children will do as their parents have been doing in front of them. Their observation of what you do is what needs to concern you the most. It is the responsibility of the parents to teach their kids proper values and the way to act responsibly. In this age of the internet, you will have to work out how our kids interact with that resource. The internet affords us so much to take. No other information and communication tool in our history compares. It however, needs one to use it well if it is to be something positive in their lives. Since they shall at some point access the internet, it is beneficial for all concerned if you can teach your kids how to interact with the resource responsibly. Here are the points that need to be driven home.
You need to show them what constitutes bad behavior, and what good behavior looks like. The same approach you use to show them right from wrong in other areas of life applies here as well. They should know how bad cyberbullying happens to be. They need to know the importance of not hurting others online. They would also not like being the ones getting hurt that way. They should learn to be kind to others. When they see a positive way of navigating the internet, any negative and malicious influences shall not stick.
You then need to institute parents controls and also find a kid-friendly search engine. This shall help you keep tabs on the websites your child visits. These also, block their access to bad and unsuitable sites. You need to tell them the right kind of websites they can visit, and what information they are allowed to share. By putting too much info out there, they put themselves in grave danger.
You then need to teach the older kids some of the laws that touch on online behavior. They will now see what consequences await those who harass others online. Another example is the grave consequence of them sharing nude photos with friends. They will be seen as violating child pornography laws, which gets them branded as sex offenders. They may have been having some fun. Under the influence of peer pressure, or facing blackmail, whatever the case, their lives will never be the same again. Speaking out beforehand should be their primary reaction.
You then need to lead by example. Kids tend to emulate more of what you do, and less of what you say. By observing how you prioritize those internet access gadgets, they shall form some strong baseline behaviors. You need to behave accordingly.