Install Firewall on your machine and restrict all the connections to the Internet (except for the anonymous proxy server) from a browser. It's also recommended to use port mapping for this free anonymous proxy server and define the browser's proxy as 127.0.0.1 with the local port from port mapping.
Use socksification in your browser. This will enable relaying all the information your browser or any other software sends and transfers to the proxy server.
3║- THE Best Method
You need to set up LAN, local IP addresses (192.168.1.x or alike). A corporate proxy server should forwards ALL requests to a free anonymous proxy server (you need to have skills and rights of a system administrator in order to do that). It's impossible to connect to the Internet bypassing a corporate proxy, as long as external IP address is not assigned to local machines. It's also impossible to scan local machine's settings: even if Java/ActiveX applets detects and gives out your local IP address (192.168.1.x) to the web server, your anonymity will remain unbroken. So, basically, you can rate this option as 100% anonymity.