Go to the Java website, choose the JRE based on your platform, download the requisite .bin files and upload them to your home folder:
su - serveradmin # If you are not already serveradmin cd ~ # Switch to the serveradmin home directory chmod +x jre-6u16-linux-i586.bin ./jre-6u14-linux-i586.bin # Decompresses JRE to the current folder under jre1.6.0_16. mv ./jre1.6.0_16
If you go with 64-bit Java (which I recommend against as it's way slower right now) I find it useful to add to the default folder name _64-bit so in that case it would be, jre1.6.0_16*_64-bit*.
For Solaris, use the sh file, and run it.
You can also do something very similar with my Windows instructions.
For older versions go to the Java Archives site.