I would strongly recommend this site:
I used this site to install java and it's plugins for mozilla, it's a very good tutorial, and if you follow it step by step, you'll have java and all it's components working in no time with mozilla. I have used it on redhat 8 and 9. And I did just as he said, and DID NOT use the rpms from sun, but instead I downloaded the "linux self-extracting binary". And everything works like a charm now... I know for sure that java applets and java-vm work like a charm, because I have used them personally.
Hope this helps,