How do I add an ID to the ul tag of a menu?
You can make use of theme_menu_tree

function theme_menu_tree($variables) {
  return '&lt;ul class="menu"&gt;' . $variables['tree'] . '&lt;/ul&gt;';
}


http://api.drupal.org/api/drupal/includes%21menu.inc/function/theme_menu_tree/7

You can print this menu tree

template_preprocess_menu_tree


hereis api

Pre process the menu tree OR Call the menu theme to print it as you want. 
Thats all.