How can I create an automatic drop down menu with my tags?

wp_list_categories is what you’re after. It takes taxonomy as an optional argument.

Example taken from Codex:

<?php 

$taxonomy     = 'genre';
$orderby      = 'name'; 
$show_count   = 0;      // 1 for yes, 0 for no
$pad_counts   = 0;      // 1 for yes, 0 for no
$hierarchical = 1;      // 1 for yes, 0 for no
$title="";

$args = array(
  'taxonomy'     => $taxonomy,
  'orderby'      => $orderby,
  'show_count'   => $show_count,
  'pad_counts'   => $pad_counts,
  'hierarchical' => $hierarchical,
  'title_li'     => $title
);
?>

<ul>
<?php wp_list_categories( $args ); ?>
</ul>