How do I add an item to the WP admin menu?

You could do it with something like this in theme functions.php (at end)

add_action('admin_menu', 'news_admin_test');
function news_admin_test() {
    add_menu_page( 'News Page Title', 'News Option', 'manage_options', 'newspage', 'show_menu_news', get_home_url() .'/wp-content/themes/my_theme/assets/img/logo.png' );
}

function show_menu_news () {
    echo 'News content';
}