Referencing an earlier post, here is the method that I have determined worked for me.

First, download the latest release of the JRE. At the time of writing, it was Java 7u10. To make things easier (they make you agree to the ToS before you can download from the website), I downloaded jre-7u10-linux-i586.tar.gz to my Windows server first, then used wget to transfer it to the Linux box, like so:

wget http://10.0.0.3/jre-7u10-linux-i586.tar.gz

Then I unpacked it, and cleaned up my mess.

tar -xvf jre-7u10-linux-i586.tar.gz
rm jre-7u10-linux-i586.tar.gz

I just went ahead and left the folder jre1.7.0_10 where it was in /home/brandon, but you can move it if you want to. Then, I made sure to adjust my path like so:

export PATH=$PATH:/home/brandon/jre1.7.0_10/bin

To test the installation, run the command java, and if you get a lengthy usage guide, you’re all set.