Back in May 2011, I saw a lot of Java EE 6 at JavaOne, Hyderabad at tech talks and a hands-on lab by Arun Gupta. So a couple of weeks back (i.e. in October 2011) I thought of giving Java EE 6 a try and I must say that Java EE 6 is amazing. Developing enterprise beans, working with web services, creating rich user interfaces etc. is a breeze.
To get started with Java EE 6, I'd recommend Antonio Goncalves - Beginning Java EE 6 Platform with Glassfish 3 from Apress. It's a great book for beginners. The author explains the concepts clearly and in an easy-to-understand manner. For more advanced learning, there is always the Java EE 6 tutorial.