You can use your browser's developer tools to see what's happening behind your back while you're visiting a web page (I recommend Firebug in Firefox). Alternatively, you may use a network spoofer like Wireshark to capture the traffic from the browser and analyze it in any way.
It's all up to you to find the information you think is relevant inside it in URLs, in request headers and bodies, etc. In your case, this would include script generated content and referal codes that may help keeping track of a user's browsing history across domains.
You don't really need Javascript knowledge to do this, but you need some basics about networking protocols.
This is probably as illegal as using a text editor, but just ask your lawyer if you're unsure :D