Note that installing Java on a Mac is performed on a system wide basis, for all users, and administrator privileges are required. You cannot install Java on a single-user basis.
A 64-bit browser (Safari or Firefox, for example) is required to run Oracle Java on Mac OS X. 32-bit browsers do not support Java 7 and later versions on the Mac platform.* Users with Mac OS X versions 10.6 and below should go to Software Update under the Apple menu to look for updates.