I understand that you are not using any Ajax calls to save the data, so the simplest way would be to set a request attribute and redirect the control to a JSP, based on the value of the request attribute you can execute a javascript call.
Using javascript in liferay is nothing different from using it in any other web-application.
Here is some sample code snippet (not the whole code):
In your portlet's action method:
// either set the renderParameter
actionRequest.setRenderParameter("saveSuccessfulPARAM", "SAVED");
// OR set the request attribute
actionRequest.setAttribute("saveSuccessfulATTR", "SAVED");
Now in the JSP which would be rendered after successful save you can have:
<%
// Note: You can use jstl or liferay tags instead of scriptlets if you want
String savedAttribute = renderRequest.getAttribute("saveSuccessfulATTR");
// OR you can use this, to fetch the renderParamter set by actionResponse
// String saveParameter = ParamUtil.getString(renderRequest, "saveSuccessfulPARAM")
if("SAVED".equals(savedAttribute)) { // if this is true show an alert
%>
<script>
// you can use <aui:script> tag as well
// .. your javascript code will go here
// better would be to run this script on DOM ready
alert("Data Saved Successfully!"); // for example
</script>
<%
}
%>
Note: It would be better to run the javascript
on DOM
ready.