If you want to add an effect, you need to edit js file:
/skin/frontend/default/default/js/webandpeople/custommenu/custommenu.js
The function: wpShowMenuPopup
The line, which is responsible for the show: popup.style.display = 'block';
The function: wpHideMenuPopup
The line, which is responsible for hiding: popup.style.display = 'none';
Examples
You can find commented examples in the js on how to manage show/hide effects.
For example in the js function wpShowMenuPopup
You can replace line
popup.style.display = 'block';
to
jQuery('#' + popupId).stop(true, true).fadeIn();
And
in the js function wpHideMenuPopup
replace line
popup.style.display = 'none';
to
jQuery('#' + popupId).stop(true, true).fadeOut();
This article is related to the Responsive Custom Menu free Magento Extension.
Custom Menu is an advanced free Magento menu with Mobile menu and flexible configuration settings that you could use for any eCommerce store.