If you know nothing about Internet safety, start by visiting the resources listed here. Educate yourself about Internet dangers and the kinds of protection available.
In terms of filtering, I recommend using the Windows Vista built-in parental controls. You can select age-appropriate access level, define time restrictions, view logs of sites visited, etc. Each user must have their own login on Vista (no sharing accounts!). If you're not using Vista, please think seriously about upgrading. The parental controls feature alone is worth the money. However, at this point in time you should probably upgrade to Windows 7 since its release date is near. I assume it has the same or even better parental controls.
Defense in depth applies in protecting children too. So for better protection, I also recommend using BlueCoat's K9 Web Protection (available for free). It is not as flexible (all users have the same filter level), but it catches some stuff that Vista doesn't. If you are currently stuck on Windows XP, use K9 at least. Just remember it is not perfect.
Finally, if you don't want a hacker opening a reverse shell and taking over your computer, make sure you check for software updates at least weekly! Or, have it done automatically if possible. These updates should include not just Windows and Anti-Virus software, but also Internet Explorer, Adobe Reader, Flash Player, Firefox, Thunderbird, Java, iTunes, etc.
