You can see this in action in the administration home page.
If you look at the corresponding admin template 'design/admin/templates/user/login.tpl' you can see for yourself the form values needed in your own script to use this feature.
That piece of code will be execute only when site.ini.[Session].RememberMeTimeout setting is set. See settings/site.ini for more details. In your case you have to configure it in settings/siteaccess/ezwebin_site_admin/site.ini.append.php, simply put