How to unpublish my new site while working on it?

If you will want to do something by you self than you will have to create a custom html or php file a redirect your site to it, this can be done by using template_include, you will have do to something like:

function coming_soon_page( $template ) {

  if (!is_user_logged_in()) {
    $cs_template = locate_template( array( 'path/to-your/comingsoon-page.php' ) );
    if ( '' != $cs_template ) {
        return $cs_template ;
    }
  }

  return $template;
}

add_filter( 'template_include', 'coming_soon_page', 99 );

You will have to put it on your theme functions.php and until you let it there the site will redirect all users not logged in to that file.

And if you will want to have some countdown function then take a look at: EASY COUNTDOWN

But if you can’t do it by your self then try using any plugin like: Ultimate Coming Soon Page