How do restrict internet access to certain user accounts?

Are you referring to user accounts on a single PC or a corporate environment with lots of users? How are you accessing the Internet?

On a PC, you could use parental control and not give them the password (and make sure that they don't have admin rights). You could also use this solution: http://www.boutell.com/newfaq/browser/restrictie.html. Here's another similar solution: http://www.howtonetworking.com/Int [...] ictie0.htm

In a corporate environment, you can restrict them through a proxy server where a user name and password are required. If you use static IP addresses, you could deny access to specific IP addresses. You can also deny access to MAC addresses, but the last two solutions work only when users are always using the same PC. You can also buy commercial software to control Internet access.