Take the Tutorial
The Pivot tutorial is a great place to get started. It covers the overall architecture of the platform, walks through a few requisite "Hello World" examples, and then proceeds to cover every Pivot component using real examples.
To follow along with the examples in the Pivot tutorial, you'll need a local copy of the Pivot 2.0.4 release. The binary and source distributions are available for download through one of Apache's mirrors.
Join the User Mailing List
The best place to get your questions answered is the user mailing list. Many people on the mailing lists have gone through the same learning curve and are ready and willing to help.
Learn About BXML
One of the benefits of using Pivot is the optional use of the GUI markup language, BXML. Its use can dramatically speed up development of visual user interfaces. To develop a firm understanding of the relationship between BXML and the Java code that it represents, we recommend reading the BXML primer.