To add a secondary menu, you need to add the following code to your child theme functions.php file.
/* secondary menu in child theme */ register_nav_menus( array( 'primary' => __( 'Primary Navigation', 'CHILDTHEME' ), 'secondary' => __( 'Secondary Navigation', 'CHILDTHEME'), ) );
Now secondary navigation will appear on back-end Appearance > Menus, in left column. You may create a new secondary menu clicking on tab with +, on top of the page. Add menu items. Remember to save the new menu. Then assign it to secondary navigation in left column pane.
Add secondary menu to your child template with this code:
// secondary menu wp_nav_menu( array('container_class' => 'SECONDMENUCLASS', 'theme_location' => 'secondary' ) );
Now we may style the second menu with CSS using the class name provided.
Update: This is also good for newest default TwentyTwelve theme! Checked.