When you say J2EE is "up and running", what do you mean? J2EE is a jar file (collection of classes) for enterprise
java. For example, it contains the code for a session.
"when I try to run the servlet on my server" What server are you using? J2EE is not a server. (You'll know that you have a server when you have something that can be explicitly started.
Yes, you need to install a server separately. Tomcat is pretty simple to use.