- You can call a Java Servlet implementation from your JSPs. (With your forms or the jsp:include and jsp:forward tags)
- You might or might not want to use EJB. (Tutorial)
- A framework is not mandatory though Spring, Hibernate and/or Struts might be useful.
If it is the first time you are using servlets, i recommend you to start with Servlet and POJOs only.
There is plenty of information here http://docs.oracle.com/javaee/6/tutorial/doc/bnafd.html