How do I retrieve the title of a term of a custom post type with custom taxonomies?

It works the same way within any Loop for any post type and taxonomy, get_the_ID() retrieves the current post’s ID. Taken from the Codex basic example for get_the_terms:

$terms = get_the_terms( get_the_ID(), 'genre' );
if ( $terms && ! is_wp_error( $terms ) ) { 
    foreach ( $terms as $term ) {
        echo $term->name;
    }
}