WordPress Enable Tags for Custom Post Type

Just add this line when you register the post type:
'taxonomies' => array('category', 'post_tag')

So something like this for all of the code:

register_post_type( 'customtype',
   array(
      'labels' => array(
         'name' => __( 'CustomType' ),
         'singular_name' => __( 'CustomType' )
      ),
      'supports' => array(
         'title','page-attributes','description','editor', 'thumbnail'
      ),
      'public' => true,
      'has_archive' => true,
      'rewrite' => array('slug' => 'customtype'),
      'taxonomies' => array('category', 'post_tag')
   )
);