Download a Sun Java virtual machine from http://www.java.com/en/download/linux_manual.jsp.
Choose the "Linux (self extracting file)", which gives a file called jre-1_5_0_06-linux-i586.bin in the home directory, or a higher version.
Open a terminal.
In the terminal, to verify the package is there, type
ls
To install the package, type
sh jre-1_5_0_06-linux-i586.bin
Agree to the license and complete installing Java.
Make a note of the directory where Java got installed. In this case this is ~/jre1.5.0_06
Note. If you install it in the directory given above, then Bibledit will find Java automatically. If you install it elsewhere, you need to enter the path to Java by hand.
Note. Some Linux distributions come with their own version of Java installed. It may be quite a hassle to find out where this version of Java has been installed, and so it may be difficult to fill in the directory in Bibledit. In case you encounter trouble to find that directory, it will be easier to just download the Java version as described above, and install it following the instructions.