Be warned: in the download process (the next step), free extra programs are sometimes offered, like a Yahoo or Google toolbar. If you do not want them to be automatically co-installed, you must unselect (=remove the tick) them in the appropriate checkbox.
You must have administrator rights on the computer to be allowed to install Java.
On the download page choose the option: "Java Runtime Environment (JRE) 5.0 Update 14".
Follow the steps of the install procedure as indicated.
Often it is necessary to close all browser-windows after the download/install and restart the browser, before Java will work. Occassionally, you might even need to restart the computer.