00-add-submenu-page.php

<?php

add_action( 'admin_menu', 'acme_add_submenu' );
/**
 * Adds the plugin menu item to the 'Tools' menu in the WordPress dashboard.
 *
 * @since     1.0.0
 */
function acme_add_submenu() {

	add_submenu_page(
		'tools.php',
		'Acme Submenu Page',
		'Acme Submenu Page',
		'manage_options',
		'acme-submenu-page',
		'acme_render_submenu_page' // This function will be defined in a moment
	);

}

01-render-submenu-page.php

<?php
/**
 * Displays the submenu page.
 *
 * @since    1.0.0
 */
function acme_render_submenu_page() {
	include_once plugin_dir_path( dirname( __FILE__ ) ) . 'admin/views/acme-submenu-page.php';
}

02-acme-submenu-page.php

<?php
/**
 * Renders the content of the submenu page for the Acme submenu page.
 *
 * @since    1.0.0
 *
 * @package     Acme
 * @subpackage  Acme/admin/views
 */
?>

<div class="wrap">

	<h1>Acme Submenu Page</h1>
	<p class="description">
		Select your options from the following set of choices...
	</p>

	<form action="" method="post">
	  
		<!-- The set of option elements, such as checkboxes, would go here -->

		<?php submit_button( 'Save' ); ?>
		<?php wp_nonce_field( 'acme-submenu-page-save', 'acme-submenu-page-save-nonce' ); ?>

	</form>

</div><!-- .wrap -->

03-acme-submenu-page-save.php

<?php

add_action( 'load-tools_page_acme-submenu-page', 'acme_save_options' );
/**
 * The method for saving the options to the database or for deleting them
 * based on what the user has specified on the submenu page.
 *
 * @since    1.0.0
 */
function acme_save_options() {

	$action       = 'acme-submenu-page-save';
	$nonce        = 'acme-submenu-page-save-nonce';

	// If the user doesn't have permission to save, then display an error message
	if ( ! acme_user_can_save( $action, $nonce ) ) {
		return;
	}
	
	/* Here is where you update your options. Depending on what you've implemented,
	   the code may vary, but it will generally follow something like this:
	 
	   if ( isset( $_POST['acme-your-option-name'] ) ) {
		 
			- Sanitize the code
			- update_option( $your_option_id, $your_option_value );
		
		} else {
			
			delete_option( $your_option_id );
			
		}
		
	*/

}

04-acme-user-can-save.php

<?php

/**
 * Determines if the user has permission to save the information from the submenu
 * page.
 *
 * @since    1.0.0
 * @access   private
 *
 * @param    string    $action   The name of the action specified on the submenu page
 * @param    string    $nonce    The nonce specified on the submenu page
 *
 * @return   bool                True if the user has permission to save; false, otherwise.
 */
function acme_user_can_save( $action, $nonce ) {

	$is_nonce_set   = isset( $_POST[ $nonce ] );
	$is_valid_nonce = false;
	
	if ( $is_nonce_set ) {
		$is_valid_nonce = wp_verify_nonce( $_POST[ $nonce ], $action );
	}

	return ( $is_nonce_set && $is_valid_nonce );

}