Yes, Ubuntu is a distro. I would recommend that you record that type of information in your profile so people do not need to ask that kind of question time and again (check my profile on the left to see what I mean).
Well, just go to System > Admin > Synaptic, enter "java" in the search box, check the box for the application(s) that you need and click on "Apply".
Alternatively, you can install from the command line:
if you enter
aptitude search sun-java
if will show which sun-java packages are available. You can install any of those with
sudo aptitude install package_name (e.g. sun-java6-jre)
Yes, you could install the software you have downloaded manually instead but you will find that the methods above are a lot more convenient. And just look at all the software you can find in synaptic! Installing things manually is just not required anymore, unless you need to do something rather exotic.
By the way, have you set up medibuntu? It contains additional codecs, google-earth, etc. Just use google to find out how to set it up, then you can install those additional packages through synaptic or the command line.
Edit: I thought you might want to have a look at this: http://ubuntuguide.org/wiki/Ubuntu:Intrepid