Wordpress - How to Add Tags to Custom Post Type?

Or just add:

'taxonomies' => array('post_tag')

An array of registered taxonomies like category or post_tag that will be used with this post type. This can be used in lieu of calling register_taxonomy_for_object_type() directly. Custom taxonomies still need to be registered with register_taxonomy().

to the $args array in the functions.php-file where you create the custom post type with register_post_type().

Like this: (Where it says "portfolio" is where you register the taxonomy to a post type

add_action( 'init', 'create_tag_taxonomies', 0 );

//create two taxonomies, genres and tags for the post type "tag"
function create_tag_taxonomies() 
{
  // Add new taxonomy, NOT hierarchical (like tags)
  $labels = array(
    'name' => _x( 'Tags', 'taxonomy general name' ),
    'singular_name' => _x( 'Tag', 'taxonomy singular name' ),
    'search_items' =>  __( 'Search Tags' ),
    'popular_items' => __( 'Popular Tags' ),
    'all_items' => __( 'All Tags' ),
    'parent_item' => null,
    'parent_item_colon' => null,
    'edit_item' => __( 'Edit Tag' ), 
    'update_item' => __( 'Update Tag' ),
    'add_new_item' => __( 'Add New Tag' ),
    'new_item_name' => __( 'New Tag Name' ),
    'separate_items_with_commas' => __( 'Separate tags with commas' ),
    'add_or_remove_items' => __( 'Add or remove tags' ),
    'choose_from_most_used' => __( 'Choose from the most used tags' ),
    'menu_name' => __( 'Tags' ),
  ); 

  register_taxonomy('tag','portfolio',array(
    'hierarchical' => false,
    'labels' => $labels,
    'show_ui' => true,
    'update_count_callback' => '_update_post_term_count',
    'query_var' => true,
    'rewrite' => array( 'slug' => 'tag' ),
  ));
}
?>

Use this:

add_action( 'init', 'gp_register_taxonomy_for_object_type' );
function gp_register_taxonomy_for_object_type() {
    register_taxonomy_for_object_type( 'post_tag', 'portfolio' );
};