The simple way is IMHO the right way:

Login by submitting the login/pass on the right page.
You'll get a session_cookie,a session id and/or another hidden field.
the cookie will be managed automagicallt by LWP, you'll have to parse
the HTML code returned to get the optionnal idetification params(id-session appended/posted to url or hidden field.)
The 'get/post' pages feeding the needed values (nothing to do for the cookie, LWP is great enough to do it for you)
You could look at this post to get an idea.

But please post your code for I can give you a more precise answer.
(beccause I gave you the more common methods to authenticate a user
though his navigation, but there are a lot of other ways (Referer, UserAgent checking...))