Where to implement custom walker class?

The walker class is an abstract class designed to help traverse and display elements which have a hierarchical (or tree like) structure. It doesn't actually 'do' (in the sense of generating HTML) anything.

in your template files, we will use the wp_nav_menu() function twice, pointing to the same theme location (I shall call it 'primary'). If you don't have a theme location registered already you should read this article. Whichever theme location you are using, you should save a menu to that location. We shall display this menu twice. First, wherever you want your 'top-level' menu to appear:

wp_nav_menu( array('theme_location'=>'primary','depth' => 1) );

Then again, with a custom walker, to display only the (relevant) child pages.

wp_nav_menu( array('theme_location'=>'primary','walker' => new SH_Child_Only_Walker(),'depth' => 0) );

I follow this example :

class SH_Child_Only_Walker extends Walker_Nav_Menu {

    // Don't start the top level
    function start_lvl(&$output, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::start_lvl(&$output, $depth,$args);
    }

    // Don't end the top level
    function end_lvl(&$output, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::end_lvl(&$output, $depth,$args);
    }

    // Don't print top-level elements
    function start_el(&$output, $item, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::start_el(&$output, $item, $depth, $args);
    }

    function end_el(&$output, $item, $depth=0, $args=array()) {
        if( 0 == $depth )
            return;
        parent::end_el(&$output, $item, $depth, $args);
    }

    // Only follow down one branch
    function display_element( $element, &$children_elements, $max_depth, $depth=0, $args, &$output ) {

        // Check if element as a 'current element' class
        $current_element_markers = array( 'current-menu-item', 'current-menu-parent', 'current-menu-ancestor' );
        $current_class = array_intersect( $current_element_markers, $element->classes );

        // If element has a 'current' class, it is an ancestor of the current element
        $ancestor_of_current = !empty($current_class);

        // If this is a top-level link and not the current, or ancestor of the current menu item - stop here.
        if ( 0 == $depth && !$ancestor_of_current)
            return

        parent::display_element( $element, &$children_elements, $max_depth, $depth, $args, &$output );
    }
}