Add a menu button to the Header, and a "Close Navigation" menu to the Primary Navigation for the off-canvas tutorial. http://www.calvinkoepke.com/add-a-mobile-friendly-off-canvas-menu-in-genesis/

functions.php

<?php
//* Do NOT include the opening PHP tag

/**
  * Add the menu to the .site-header, but hooking right before the genesis_header_markup_close action.
  * @author Calvin Koepke (@cjkoepke)
  * @link http://www.calvinkoepke.com/add-a-mobile-friendly-off-canvas-menu-in-genesis
*/
add_action( 'genesis_header', 'ck_menu_button', 14 );
function ck_menu_button() {
	
  //* Only add the Menu button if a primary navigation is set. You can switch this for whatever menu you are dealing with
  if ( has_nav_menu( "primary" ) ) {
    
    echo '<a alt="Toggle Menu" href="#" class="menu-btn right small">' . __( 'Menu', 'CHILD_THEME_TEXT_DOMAIN' ) . '<span class="dashicons dashicons-menu"></span></a>';
  
  }
  
}

//* Add the "Close Navigation" text to the Primary menu output.
add_filter( 'genesis_nav_items', 'ck_close_btn', 10, 2 );
add_filter( 'wp_nav_menu_items', 'ck_close_btn', 10, 2 );
function ck_close_btn($menu, $args) {
  
  $extras = '<a href="#" class="close-btn"><em>' . __( 'Close Navigation', 'CHILD_THEME_TEXT_DOMAIN' ) . '</em> <span class="dashicons dashicons-no"></span></a>';
  
  if ( $args->theme_location == "primary" ) {
    
    return $extras . $menu;
  
  } else {
  
    return $menu;
  
  }
  
}