The Java Runtime Environment (JRE) is required if you need to run any java-based applications on your Ubuntu machine. Many times this is required for certain websites and is always a good addition to your installed package base. To install the Java Runtime Environment including the plugin for Mozilla Firefox simply run the following command. (note: you will need to have additional repositories enabled. See How to add extra repositories.
sudo aptitude install sun-java6-jre sun-java6-plugin sun-java6-bin
You will have to agree to the DLJ license terms to install this package. To find out more about the terms of the DLJ visit the DLJ FAQ.