First off, install the Sun Java2 RE (or SDK), either by RPM or self-extracting binary (my preference). I stick the SDK in /usr/local/j2sdk1.4.1 and then test that it works:
$ /usr/local/j2sdk1.4.1/bin/java -version
If it does work, then the easiest way to install the Java Plugin is to create a symlink, i.e.
# ln -s /usr/local/j2sdk1.4.1/jre/plugin/i386/ns610/libjavaplugin_oji.so /opt/mozilla/plugins
This is the old way to install the Java Plugin, but for silly technical reasons, it's still the way to go.
FYI, Java in Mozilla works just fine. I don't use KDE so I can't comment on enabling the Java plugin, but you can search google. Any Java applets that don't work well with the Sun Java2 VM were probably targeted for the Microsoft VM, which is a terrible mistake.
Edit:
Fixed typo. Thanks Gooberlx2.