Child protection advice (in brief)
There are no easy and quick answers here, but both the Child Exploitation and Online Protection centre (CEOP) and Childnet agree that parents and children should be talking together about the issues and about what the child is doing on the internet, even if the parent is not particularly knowledgable about IT matters. The PC should preferably be in a room commonly used by both parents and children and not in the child's bedroom.
There needs to be supervision and discussion of the issues because there is no technical fix to the problem. It is possible to put software on the the PC which can control access to websites, but this can never be 100% effective, and technically savvy children may find ways around this.
Essentially this is a people problem not a technical problem, and just as when warning children about going with strangers, it is necessary to encourage them to be cautious and thoughtful rather than trusting. Compared to the huge use of the internet by young people the instances of abuse or exploitation are small in number, but they do happen and children need to be warned about it.