Java for i386
Add the hoary-extras repository (AddingRepositoriesHowto)
Search for sun-j2re1.5 in synaptic and install it.
This will configure the Firefox Java plugin. Alternatively, you can build your own Java package by following the instructions on JavaPackageBuildNewVersions.
In BreezyBadger, Java is available as the j2re1.4 and j2se1.4 packages in the multiverse repository. In order to get Java plugins working in your browser, you may have to manually install libxp6 until the [https://launchpad.net/malone/bugs/2183 relevant bug] in the packaging gets fixed.
Java on other Architechtures
Ubuntu PPC, please see: ["JavaPPC"]. Ubuntu AMD64, please see: ["JavaAMD64"].
Installing the JDK
If you want to install the Java compiler as well as the runtime environment, the easiest thing to do is to [https://java.sun.com/j2se/1.5.0/download.jsp get it directly from Sun]. Take care to use the "Linux self-extracting file" version. Converting the RPM with alien will not work.
Then follow the instructions as set forth on JavaPackageBuildNewVersions to create a .deb file you can install using dpkg.