The .bin file is just a tar/gzipped file wrapped in a shell script. Set the file executable and run it to decompress the Java2 RE (into the current directory). For example:
# Unpack as user
$ chmod u+x /path/to/j2sdk-1.4.0_01.bin
$ mkdir /tmp/j2sdk-1.4.0
$ cd /tmp/j2sdk-1.4.0
$ ./j2sdk-1.4.0_01.bin
# Install as system JRE as privileged user
$ su
# mv /tmp/j2sdk-1.4.0 /usr/local
# chown -R root.root /usr/local/j2sdk-1.4.0
Only thing left is to add /usr/local/j2sdk-1.4.0/bin to your users' PATH or build environment. Installing the Java2 Plugin into your web browser is a separate, optional step as well.
You can download an .rpm version (not the .bin) but historically the .rpm offers minimal advantages.