JPython's home is http://www.jpython.org/, which is a sister site to http://www.python.org/. It is the main place to obtain JPython information, download the code, find out about CVS access, read the JPython-specific documentation, and learn about the jpython-interest mailing list. Detailed installation instructions are available on the web site and will not be repeated here.
JPython requires you to have a JVM (Java Virtual Machine) installed to run the installer, which is a compiled Java program. The JVM is the program at the core of running compiled Java code. Sun Microsystems publishes the specifications a “compatible” JVM must follow, and they and others provide JVM implementations. JPython requires a complete and bug-free JVM. Finding such a JVM can be a challenge, depending on the operating system you're using. On Windows, you can use either Sun's JVM or Microsoft's. Linux users should use the JVM, originally developed by the Blackdown initiative and currently maintained and distributed by Sun. This JVM now includes Inprise's Just-In-Time compiler for better performance.
Once the JVM is installed, you can install JPython. There are two versions of the self-extracting installer which can be downloaded: one with OROMatcher and one without. OROMatcher is a regular-expression library which gives JPython regular expressions power that matches CPython's. JPython is open source, but the source to OROMatcher is not available, and redistribution of the OROMatcher classes separately from JPython is not allowed. Most users should get the version with OROMatcher.
Finally, you may want to download the Python standard library (the .py files which come with any Python installation), or you can configure JPython to use an existing CPython's standard library tree.
As of this writing, the current version of JPython is 1.1. It would not be fair to omit mentioning bugs. JPython is not as mature as CPython, and JPython's buglist is quite a bit larger than CPython's, especially when it comes to the jpythonc tool. On the plus side, JPython's source code is quite a bit shorter than its older brother's, so the number of places for bugs to hide is smaller.