when you register a taxonomy, the second argument is the post type it is available for:
register_taxonomy( $taxonomy, $object_type, $args );
if you want the taxonomy to work for a custom type as well as standard posts, you can pass an array of types:
$object_type = array( 'your_custom_type', 'post' );
alternately, you can use register_taxonomy_for_object_type
:
register_taxonomy_for_object_type( 'your_custom_taxonomy', 'post' );