Some time ago I did a short talk on Google Guava for our local JUG. It was a basic intro into Guava and how it makes stuff simpler, better and cleaner.

It is true that there is an overlap with Apache commons but Guava is build with expectation that there is a Function and a Predicate class as well as various builders which makes it really cool and simple for many use cases.
The talked covered most of the com.google.common.base.* classes  and basic use of functions in collection and Google collections  and few other features that are part of Guava and I find them very useful.
Source code of the examples can be found on github and here is the actual presentation:

Note one last recommendation that is not just mine but  also part of Guava's wiki :

Excessive use of Guava's functional programming idioms can lead to verbose, confusing, unreadable, and inefficient code. These are by far the most easily (and most commonly) abused parts of Guava, and when you go to preposterous lengths to make your code "a one-liner," the Guava team weeps.

 


Related links 

• http://code.google.com/p/guava-libraries/
• http://code.google.com/p/guava-libraries/wiki/UseGuavaInYourBuild
• https://github.com/mitemitreski/guava-examples
• http://stackoverflow.com/questions/tagged/guava
• http://www.tfnico.com/presentations/google-guava#TOC-Presentation
• http://gdg-krakow.github.com/google-io-ext-2012-guava/