Sites like anonymizer will help. You could use a public proxy server just for surfing the internet also. It's easy to configure under IE and Netscape. You could setup your own proxy server and spoof your IP. You have to know what you're doing though and have the software. These will only help hide your IP from the sites you're surfing and they're very basic approach to doing it.
Basically, if you do something severe, it can and will most likely be traced back to the computer you used to do it. If not by IP than by a MAC address, which is hard coded into the NIC on the computer.
If you're concerned about your Network Administrator at work seeing where you're surfing, then you're shit out of luck. Unless they don't actively monitor the desktops/employees.