WebObjects/Database Compatibility and Comparisons/Postgresql< WebObjects
Yes, PostgreSQL does work with WebObjects. The best place to start is the Project WONDER PostgresqlPlugin Page.
If you're on a Mac, Apple has an article on installing PostgreSQL on Mac OS X that is pretty straightforward.
If you're interested in a nice graphical interface to managing your PostgreSQL installation, you may want to checkout out Navicat PostgreSQL from Navicat.