The basic idea behind making any plugin work on a Mozilla based browser is to have the plugin symbolically linked to the plugins directory of Mozilla or Firefox. Fedora 10 already has the Sun JRE (Java Runtime Environment) JRE 1.6.0_07 packed in the box. Now, in order to enable the java plugin on your firefox do the following steps:
1) locate the file named libjavaplugin.so (or libjavaplugin_oji.so in some cases) on your box by issuing the following command at the prompt:
you`ll find that the file libjavaplugin_oji.so is available in the /usr/java/jre1.6.0_07/plugin/i386/ directory.
2) Then what you need to do is just link the .so file symbolically to the mozilla plugins folder, and you are done:
3) Restart your browser and head over to http://www.java.com/en/download/installed.jsp to verify if your plugin installed successfully or not. (Don`t worry, It will)
PS: I would recommend you to install the latest version of the Sun JRE, ie. v1.6.0_11. You may also like to read about how to get the flash plugin on Firefox to work on linux here.