Need help with menu for member and non-member

I am working on A website and I am kinda new to HTML/PHP and some CSS. My question is I found code to add a menu for members that are logged in and ones that are not see a different one http://www.techknot.com/4466/show-different-menu-items-to-logged-in-users.html. My issue is knowing where to put it and If I need to replace or remove any code from original code in the functions.php file. Below I posted the navigation code from file

// Menu functions with support for WordPress 3.0 menus
if ( function_exists('wp_nav_menu') ) {
    add_theme_support( 'nav-menus' );
    register_nav_menus( array(
	'primary' => esc_html__( 'Primary Navigation', 'udesign' ),
    ) );
}

function udesign_nav() {
    if ( function_exists( 'wp_nav_menu' ) )
	wp_nav_menu( array( 'container_class' => 'navigation-menu',
			    'container_id' => 'navigation-menu',
			    'menu_class' => 'sf-menu',
			    'link_before'=> '<span>',
			    'link_after' => '</span>',
			    'theme_location' => 'primary',
			    'fallback_cb' => 'udesign_nav_fallback' )
			);
    else
        udesign_nav_fallback();
}

function udesign_nav_fallback() {
    global $udesign_options;
    $menu_html = '<div id="navigation-menu" class="navigation-menu">';
    $menu_html .= '<ul class="sf-menu">';
    $menu_html .= is_front_page() ? "<li class='current_page_item'>" : "

<li>";
    $menu_html .= '<a href="'.get_bloginfo('url').'"><span>'.esc_html__('Home', 'udesign').'</span></a></li>
';
    $menu_html .= wp_list_pages('depth=5&title_li=0&sort_column=menu_order&link_before=<span>&link_after=</span>&exclude='.$udesign_options['excluded_paged_from_menu'].'&echo=0');
    $menu_html .= '';
    $menu_html .= '</div>';
    echo $menu_html;
}

[In future please highlight your code and then press the “code” button before posting]