my $m = WWW::Mechanize->new();

# point to the url of the login form
$m->get("http://www.mydomain.com/login_form.html");

# submit form with data specified
$m->submit_form(
   form_name => "login_form",
   {
      username => "xxxxxxx",
      password => "yyyyyyy",
   }
);

# now you are logged in.
# do actions that you need to be logged in for
$m->get("http://www.mydomain.com/program.cgi?something");
# or
$m->follow_link( text => "Click here to perform some action");