I have already blogged about Installing Apex Listener on Tomcat and Managing Apex Listener.
If you have already installed Apex Listener 1.1 or temporarily want to connect to multiple databases then you can follow the steps.
1. Decide on the deployment name. Default one is /apex/. Select another one like /testdb/. Once you decide on the deployment name, goto <Tomcat Home>/webapps folder on your PC/Linux VM etc. and copy apex.war to testdb.war.
2. Configure the new Database Connection by accessing http://localhost:8080/testdb/listenerConfigure
Tomcat will automatically extract testdb.war content and will create testdb folder inside webapps.
Then it will give you a surprise and will say
"The APEX Listener is already configured. Please login as Administrator to access APEX Listener Administration." Let's fix it.
3. Open up <Tomcat Home>/webapps/testdb/WEB-INF/web.xml and configure "config.dir" as follows.
<param-value><Your Tomcat Home>/webapps/testdb</param-value>