The java plugin is installed by default in slackware. It doesn't work because mozilla doesn't know it exists.

To fix it, do the following as root:
ln -sf /usr/lib/jdk1.5.0_01/jre/plugin/i386/ns7/libjavaplugin_oji.so /usr/local/mozilla/plugins

Note that the path to mozilla is different on my system because I don't use slackware packages for mozilla. Do the following to find your mozilla directory and replace it in the above command:
find / -name mozilla 2> /dev/null

Enjoy.