Basic things are just as simple in JSP as they are in ASP. But to really take advantage of JSP pages you need to know Servlets. I recommend getting Jason Hunter's book on Servlet Programming. It is definitely the best book written on the subject. In the beginning it may all be a bit confusing but it will definitely make you a better programmer and allow you to take full advantage of JSP.
The important thing is to realize where JSP falls in the grand scheme. JSP should really only be used for presentation. Any real logic should be done in EJB/Beans and possibly Custom Tags (though I am not a real big fan).
I find that the Model-View-Controller (MVC) pattern works like a charm with JSP. EJB/Beans serve as the Model, JSP is the View, and Servlets take the role of Controller. For a good introduction to MVC as it relates to JSP/Servlets read Hans Bergsten's JavaServer Pages. I am not thrilled with the technical detail of the book but it is a good introduction for beginners on JSP and MVC.
Wushutwist