Some home routers support firewall/filtering rules, but you have to get into the router to set it up and still, the problem you have is if you have unsecured wireless networks around.
Lastly, you can install filtering software on the computer. This is an option only if you make sure your child is not an admin on the machine. A problem especially in the Windows world. But either way, with the child being an Admin, anything can be installed or uninstalled which is a BIIIG problem since kids have a habit of clicking all over the place whenever any type of advertisement or fake warning (you know the type...."Your computer is not running 100%, click here to make it faster") pops up while web browsing....Not to mention the virus threat of transferring files all over the place using IM. So...what to do? Sure there are lots of Windows solutions out there...but what about OSX? Here is one solution that works for both!
Lightspeed Guide is a product of Lightspeed Systems which make a filtering and anti-virus product for Window/OSX/Linux. They also have a home filtering option for school districts that opt to send laptops home with kids and require to maintain logging and filtering called the LightSpeed Guide.
They offer a free LightSpeed Guide as well which you can get from here. You log in to their site and create accounts for your children, then you can go and modify the filtering policy using one or more of their over 100 categories, or just choose a preset policy.