I came across a couple of posts. Some had different solutions for different versions (3.5, 3.6) of Firefox, and they also wanted me to use IcedTea. The solution I used is outlined here, and it worked perfectly well for me.
Note: You may not have libnpj2.so in the same place mentioned below.
ln -s /usr/lib/jvm/jre1.6.0_12/lib/amd64/libnpjp2.so ~/.mozilla/plugins/