Uncaught ReferenceError: jQuery is not defined . How do I define it correctly?

Just use deps parameter to include jQuery, change your code to:

    function add_my_css_and_my_js_files() {
        wp_register_script( 'validate', plugins_url( '/validate.js', __FILE__ ), array( 'jquery' ) );
        wp_enqueue_script('validate');
    }
    add_action( 'wp_enqueue_scripts', "add_my_css_and_my_js_files" );