This week's giveaway is in the EJB and other Java EE Technologies forum. We're giving away four copies of EJB 3 in Action and have Debu Panda, Reza Rahman, Ryan Cuprak, and Michael Remijan on-line! See this thread for details.
And a very good book for beginners is the "Apache Tomcat Bible" from Eaves, Jones and Godfrey. This book explains how to download and install Java, Tomcat, MySQL, Ant, Eclipse and other stuff you might need to build a web application. But the most important thing is that it gives you an overview of a web application built following the design principles of the Model-View-Controller. A must have, if I may say so.