Use apt-get install sun-java6-jre sun-java6-jdk. Just because Oracle's (Sun's) JDK distribution also contains a JRE does not necessarily mean that the Ubuntu team packaged it the same way.
Of course, if you do not want to develop Java applications on your server but only want to run them, sun-java6-jre should be enough.
The above three steps can also be performed in the gui:
System --> Administration --> Software Sources
Open the Other Software tab
Click + Add...
Enter deb http://archive.canonical.com/ lucid partner
Click +Add Source to accept the new repository
Click Close to update the source list
Open Firefox and open the following URLs:
apt:sun-java6-jre
apt:sun-java6-plugin
apt:sun-java6-fonts
Alternately, if you want to develop in java, you would install the sun-java6-jdk package.
If you have multiple versions of java installed, you may need to change the default version with the sudo update-alternatives --config java command, selecting the one with j2re1.6-sun in it.
Best Answer
You can install the Java Development package group using