This is part of a script that I wrote for getting data from a password protected site. The site uses cookies for the logins, and the password URL can be passed straight in via the URL as GET parameters.

use LWP::UserAgent;
use HTTP::Cookies;

$ua = LWP::UserAgent->new;
$ua->cookie_jar(HTTP::Cookies->new(file => "$cookie_file",
                                     autosave => 1));
$ua->timeout($url_timeout);
$res = $ua->request(HTTP::Request->new('GET', "$login_url"));

if ($res->is_error()) {
     $response = $response->status_line;
     exit;
 }
 
$response = $ua->request(HTTP::Request->new('GET', "$data_url")); 
if ($response->is_error()) {
     $response = $response->status_line;
 }
 else {
   # do what you want to do with the pages here
}
[download]

First I create a "cookie jar" which retains the cookie submitted by the site login mechanism.. Then, I submit the login_url, which is a complete URL escaped string. Thereafter, if the login is successful, I can navigate to any of the protected URLs..
HTH