Once they're on an approved site, it's up to you to teach them to follow the guidelines recommended and to adhere to your parenting rules. In addition to checking their privacy settings, teach your kids not to "click" to install anything, ever (especially when it says you need it to watch the funny cat video). It's a trap for downloading "bad" software that will infect your computer. You should also set the PC to routinely run current antivirus and antispyware software. Many Internet providers also provide parental control software so please check with your provider.
While these tools help to keep your child safe, it is ultimately up to you, as the parent, to keep your child safe by directly monitoring what your child is doing on the Internet. No Web controls can take the place of active parental involvement and oversight.