Sample code to illustrate how to instantiate the Software Licensing plugin updater class in your plugin.
<?php

/*
Plugin Name: Sample Plugin
Plugin URI: http://pippinsplugins.com/
Description: Illustrates how to include an updater in your plugin for EDD Software Licensing
Author: Pippin Williamson
Author URI: http://pippinsplugins.com
Version: 1.0
License: GNU General Public License v2.0 or later
License URI: http://www.gnu.org/licenses/gpl-2.0.html
*/

/**
 * For further details please visit https://docs.easydigitaldownloads.com/article/383-automatic-upgrades-for-wordpress-plugins
 */

// this is the URL our updater / license checker pings. This should be the URL of the site with EDD installed
define( 'EDD_SAMPLE_STORE_URL', 'http://easydigitaldownloads.com' ); // you should use your own CONSTANT name, and be sure to replace it throughout this file

// the download ID for the product in Easy Digital Downloads
define( 'EDD_SAMPLE_ITEM_ID', 123 ); // you should use your own CONSTANT name, and be sure to replace it throughout this file

// the name of the product in Easy Digital Downloads
define( 'EDD_SAMPLE_ITEM_NAME', 'Sample Plugin' ); // you should use your own CONSTANT name, and be sure to replace it throughout this file

// the name of the settings page for the license input to be displayed
define( 'EDD_SAMPLE_PLUGIN_LICENSE_PAGE', 'pluginname-license' );

if ( ! class_exists( 'EDD_SL_Plugin_Updater' ) ) {
	// load our custom updater
	include dirname( __FILE__ ) . '/EDD_SL_Plugin_Updater.php';
}

/**
 * Initialize the updater. Hooked into `init` to work with the
 * wp_version_check cron job, which allows auto-updates.
 */
function edd_sl_sample_plugin_updater() {

	// To support auto-updates, this needs to run during the wp_version_check cron job for privileged users.
	$doing_cron = defined( 'DOING_CRON' ) && DOING_CRON;
	if ( ! current_user_can( 'manage_options' ) && ! $doing_cron ) {
		return;
	}

	// retrieve our license key from the DB
	$license_key = trim( get_option( 'edd_sample_license_key' ) );

	// setup the updater
	$edd_updater = new EDD_SL_Plugin_Updater( EDD_SAMPLE_STORE_URL, __FILE__,
		array(
			'version' => '1.0',                    // current version number
			'license' => $license_key,             // license key (used get_option above to retrieve from DB)
			'item_id' => EDD_SAMPLE_ITEM_ID,       // ID of the product
			'author'  => 'Easy Digital Downloads', // author of this plugin
			'beta'    => false,
		)
	);

}
add_action( 'init', 'edd_sl_sample_plugin_updater' );