"How much?" That is the question that every parent must answer about the control they exercise over their children's internet usage. How much should parents restrict a child's website access? How much should they monitor the websites their child visits? How much should they be monitoring email and chat to ensure their child's safety? Taking an authoritarian approach will certainly help to keep the child safe, but it sacrifices privacy. On the other hand, being overly lax about monitoring can be equivalent to leaving them alone in a strange city - that kid's toast.
What it comes down to is trust. A parent cannot reasonably trust their five year old to make decisions about people who are safe to interact with, nor about content that is suitable for viewing. However, a sixteen year old should be capable of such decisions. This is where trust comes in. Some sixteen year olds will, over time, demonstrate their ability to make responsible decisions, on and off the computer. They should be given your full trust, and only receive the occasional check on browser history. Other sixteen year olds will have demonstrated themselves less trustworthy than a five year old, and should be closely monitored, or restricted from the computer altogether. There is an entire spectrum in between these two extremes, and the level of monitoring should correspond to their ability to be responsible.
Before I finish, I'd like to add one caveat. No matter how much trust a child has earned from their parents, as long as they are under your care, the computer should be placed in a location where it is visible to anyone. It's not even necessary to scrutinize what is on the screen, the presence of others in the room is enough to make a child think twice when tempted to be irresponsible online. Privacy and safety are both important, but as a parent your responsibility is primarily to the latter with a balance to the former.
