1. You could use Richfaces 3.3.4.Final (downaload here).
This is way you should include, register and use libraries in a project. Notice:
A JSF application with RichFaces assumes that the following JARs are available in the project: commons-beanutils-1.7.0.jar, commons-collections-3.2.jar, commons-digester-1.8.jar, commons-logging-1.0.4.jar, jhighlight-1.0.jar.
Example (from developer guide) for your case:
<h:form id="planetsForm">
<h:outputLabel value="Select the planet:" for="planets" />
<h:selectOneMenu id="planets" value="#{planetsMoons.currentPlanet}" valueChangeListener="#{planetsMoons.planetChanged}">
<f:selectItems value="#{planetsMoons.planetsList}" />
<a4j:support event="onchange" reRender="moons" />
</h:selectOneMenu>
<h:dataTable id="moons" value="#{planetsMoons.moonsList}" var="item">
<h:column>
<h:outputText value="#{item}"/>
</h:column>
</h:dataTable>
2. Example of other solution:
You could use jQuery.ajax() with custom servlet.
JS:
$.ajax({
type: 'GET',
url: '/app/customservlet.jsf?value=' + selectOneValue; //selected value
});
Servlet:
@Override
protected void doGet(HttpServletRequest req, HttpServletResponse res) {
String selectOneValue = req.getParameter("value");
//do something
}