Just go to the link below and click on the 'Download' button in the top right of the screen. (Green box called "Free Download >> Java software for the desktop". When you click on the link it should send you to a page where the proper java runtime will automatically download and install.)
Mozilla uses the Sun Java environment instead of having a 'proprietary' engine like IE. So you can always find out what the latest one is by visiting www.mozilla.org and seeing what they are recommending (and linking to) for Mozilla.