According to the HTTP::Proxy documentation, it will by default listen on port 8080. So you'd set your web browser to proxy through http://localhost:8080/.

Now if you're already behind a proxy (which I think is what you're implying) then you may be in for more headaches. I think that HTTP::Proxy should honor the http_proxy environment variable for connecting up-stream (since it sits on top of LWP itself; i.e. have export http_proxy=http://localhost:8118/ in the environment from which you run your proxy script). Someone more familiar with it may chime in about that, but I'd guess it would work.