One of your most important jobs as a parent is to raise your children as responsible and independent internet users. To do that, they need your help. Sit with your kids when they go on the internet, help them find their way online and show them how to deal with things they feel uncomfortable with. Look for appropriate material and help your child make a choice in the enormous offer. Find out what the age ratings of games, movies and the like are. Agree with your child to talk to you when he/she encounters something strange or inappropriate on the screen.
When they get older and more sociable, keep an eye on who your children chat and play games with. Are they friends or strangers? You are supposed to guide them, not catch them when they do something wrong. If your children think you're spying on them, they will be less inclined to talk to you when things go wrong.