I have created a menu in Drupal 7 and created links to pages under that menu.
I named my new menu \"Site Menu\"
In my page.tpl.php where I want my menu to appear
Berdir answer is correct. Drupal 7 theme_links function also more vastly uses arrays. For example if you would like to add another class name to the so that it is you would code it like this:
menu_navigation_links('menu-site-menu'), 'attributes' => array('class'=> array('links', 'site-menu')) ));?>