What browser are you using? I primarily use Firefox, but for both FF and IE you can go into the Options, then connection settings and manually enter the IP of a proxy server. FF also has several extensions that will do things like import a list of proxies from a text file, and then select which proxy to use from within the extension - extension takes care of changing the FF settings. You can also research utilities like Tor and Privoxy, which connect to a public network of proxy servers - you then add an extension to FF to use Tor.
Note that this may make your browser use the proxy, but then things like opening streaming media into Windows Media Player may bypass the proxy server unless you configure those separately.
To check if you're anon after enabling the proxy, you can go to various sites like http://www.my-proxy.com/com/info.php
or showmyip.com, which will check what your IP appears to be from their point of view.
I found my-proxy.com to be a good resource for finding out a lot more about proxies. Note that even if they show your IP as something other than your *real* IP, other details about your connection may be leaked by the proxy server. It's not easy to find proxy servers that can actually make you 100% anonymous.