How do I echo all of my taxonomies?

Function wp_get_post_terms returns array (or WP_Error but we ommit it here) so you need go through the returned array and print all items:

$skill_list = wp_get_post_terms($post->ID, 'skill', array('fields' => 'names'));
print_r( $skill_list );

Of course you can also yous for or foreach for better printing…