How to Enable Java Applet Plug-in Using Mac OSX 10.7 Lion
How to Enable Java Applet Plug-in Using Mac OSX 10.7 Lion & 10.8 Mountain Lion
Open your web browser and go to www.java.com. (or just click the link)
Click on the Free Java Download button.
Click on the Agree and Start Free Download button.
When the download is completed you will need to double click the installation file from the download window. The file will be named something similar to the screenshot below.
When the installation file opens, double click on the Java installation package icon.