Java is downloadable and redistributable from Sun, but only for personal and not-for-profit use. Sun's Java license is non-open-source, so Fedora and most other Linux distributions won't carry it.
Fedora Core 5 includes an open-source Java implementation for programmers called gcj. You only need to take special action if you want to enable applets in your browser. The Unofficial Fedora FAQ has detailed instructions on how to do this.
You can test your Java plugin at Sun's Applets page. Note that some of these applets (Escher and Starfield, when I checked) appear to be broken. BouncingHeads makes a good test.
You might also want to copy the RPMS you built out of
/usr/src/redhat/RPMS/ so you'll have then handy for