How do I simulate this to get to the information I want to extract actually?

With great patience and attention to detail.

It's just about impossible in the general case. Have a look at the WWW::Mechanize::FAQ, on the section "why don't you support JavaScript?". In a nutshell, you need to reimplement a JavaScript engine, and that's a non-trivial undertaking.

The usual way of going about automating a website that makes heavy use of JavaScript is to insert an HTTP::Proxy-based proxy between your client and the server, to record precisely what is being passed back and forth. At the lowest level, it's just GET, POST and following redirects, and doing the same thing in your program.

But depending on the site, this can be very difficult to do.