Being fairly new to Drupal I do not know how to find the $id and $pid parameters to make theme_nice_menu work on my site. Can you enlighten me?
The $id argument is the ID of the menu block you want to display. You may define how many different Nice Menus blocks, up to 10, in the settings at Administer > Site configuration > Nice Menus (example.com/admin/settings/nice-menus.) You can find the ID for a particular block you have created by going to Administer > Site building > Blocks (example.com/admin/build/block) and hovering over the "configure" link (e.g. example.com/admin/build/block/configure/nice_menus/1.) The $id for the theme function is that end number.
The $pid argument is the identifier of the menu item which is the parent of the items you want to display. You may find a menu id by going to Administer > Site building > Menus (example.com/admin/build/menu) and hovering over the edit link of the parent menu item which will end, again with a number (e.g. example.com/admin/build/menu/item/edit/10, giving 10 as the $pid for the Create content menu.)
Calling the function
The function should be called using the theme function and may be called from either the template.php or directly in a template file (like page.tpl.php.)
This example is theming the Nice menu block ID of 1 and just the menu items that belong to the Create content part of the menu and setting the menu direction to down.
$menu = theme('nice_menu', 1, 10, 'down');