Since Mozilla dropped support on OJI (Open Java Virtual Machine Integration), the classic java plugin file javaplugin-oji.so doen’t work anymore for Firefox versions >3.6. Starting in Firefox 3.6, Mozilla will only support the standard NPAPI and NPRuntime interfaces.

However, a ‘Next-Generation Java plugin’ (that’s what Sun calls it) is available in Java version 6 update 10 or newer and supports the NPAPI and NPRuntime interfaces.

Installation is quite simple. Remove the symbolic links to libjavaplugin_oji.so from the Firefox plugins directory and replace it with to libnpjp2.so:

cd ~/.mozilla/plugins/
rm -f libjavaplugin_oji.so
ln -s <JRE>/lib/i386/libnpjp2.so . 

where <JRE> is the path to your Java runtime environment.

Resources:
http://java.sun.com/javase/6/webnotes/install/jre/manual-plugin-install-linux.html