Applications menu => Add/Remove (or: System => Administration => Synaptic)
Then if you use Add/Remove tool, select from the top side's drop-down list the "Everything" option which shows every possible app available (not just the "officially supported" ones), type "jre" into the search field, wait a moment, and "Sun Java Runtime" should come to the results list. Check it and hit the Apply button.
Or if you used Synaptic, click Search, search for "jre" or "java runtime", wait for the results, select the appropriate java runtime package to be installed and click Apply.
Easy as that. Works trough command line also, if you know the package name:
sudo apt-get install packagename
NOTE: it is possible to visit Sun's website too, download their Java runtime installer package and run it (in a command prompt?), and have it install itself to the system. However it's easier to use Add/Remove or Synaptic (in general: apt, the package manager), and in addition it allows for easy updating of the package should an update come to the internet reposities of Ubuntu later. In case of a "manually" installed JRE package you should track when it's updated and repeat the installation process. I'd say stick to the Ubuntu's package manager tools when you can, and you're easier off.