Retrieve Custom Taxonomies with Description and Slug

Here’s how you can output all the custom taxonomies in any template for examination:

<pre>
    <?php 
    $args = array(
      'public'   => true,
      '_builtin' => false
    ); 
    $taxes = get_taxonomies( $args, 'objects');

    foreach ($taxes as $key => $tax) {
        $terms = get_terms( $tax->name, array('hide_empty' => false) ); // return empty ones too!
        foreach ($terms as $key => $term) {
            echo 'term ID ' . $term->term_id . ', term name: ' . $term->name . ', description: ' . $term->description . '<br/>';
        }
    }
    ?> 
</pre>

Please note that depending on how your custom taxonomies were defined your public value may need to be changed to false. Just try both.

Edit: get_terms() will allow you to get all terms for the particular taxonomy.