You should have no particular problem installing java. Just grab it here and install.

The only known problem is with sites that try to detect the availability of java through Javascript with a broken function. The consequence is that these sites won't use Java.

Bug 578 is now fixed in version 0.8.2 .

Notes:

• by Marc: If java is installed and is working in IE (you should be sure that IE is not using windows/MS older library) but not in KM, or other gecko-based browsers, check your registry. The following key should exist.
  It should have been created when KM was installed.

HKEY_LOCAL_MACHINE\Software\mozilla.org\Mozilla\CurrentVersion