what you need is an http client script that supports redirection. you pass the urls you want to visit via the query string. then you modify the links on the page returned by the http client.
e.g.
<a href="http://www.somewhere.com/somepage.html">
becomes
<a href="http://www.yourserver.com/yourscript.php?url=[urlencoded href value above]
do this for both relative and absolute urls. then you send it back to the browser. note that images will load directly from the origin server not from yours, of course you can easily fix that.
i havent really had the time to figure out how to handle forms. but for simply loading pages and following links this approach works well.
this is not theory, this was my very first task i was assigned where i work today.
good luck!