How do I get my Java GUI to use a C++ library?

The low-level route is to write a JNI wrapper for your library, though this is a lot of work.

Somewhat simpler is to generate Java bindings using a generator like SWIG.

Another option is to wrap your library up in a small executable process, and communicate between the Java and C++ processes via Sockets/Pipes/etc. (sort of like Chrome's multi-process model).

thank you swiftcoder!