I found a great blog post by Tom Petrus that summarizes the power of the APEX tree here: http://tpetrus.blogspot.be/2013/01/working-with-tree-in-apex.html
The post details a number of different attributes of the tree and how to interact with it. It starts simple and shows how to get a tree reference and gradually gets more and more detailed, including how to search the tree and how to handle when a node is selected or even double clicked.
There's a working demonstration that goes with the post here: http://apex.oracle.com/pls/apex/f?p=54687:LOGIN
Many of the techniques and tips here have been invaluable to me in recent days as I work on a new project that heavily involves using trees. Thanks, Tom!