LWP is very useful, but for your purpose you might be better off using WWW::Mechanize.

It abstracts away a lot of parsing and HTTP stuff, so you can do this (from the docs):

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

    $mech->get( $url );

    $mech->follow_link( n => 3 );
    $mech->follow_link( text_regex => qr/download this/i );
    $mech->follow_link( url => 'http://host.com/index.html' );

    $mech->submit_form(
        form_number => 3,
        fields      => {
            username    => 'yourname',
            password    => 'dummy',
        }
    );

    $mech->submit_form(
        form_name => 'search',
        fields    => { query  => 'pot of gold', },
        button    => 'Search Now'
    );
[download]