When you surf the internet your privacy basically goes out the window. One of the easiest ways to hide your computer, and thus hide you, while on the web is to use proxies. Proxies act as a computer between you and the rest of the web. When you are surfing the web through a proxy, any web servers you connect to, actually think you are connecting from the proxy computer.
See How to Surf the Web Anonymously With Proxies for simple instructions on how to do this.