There's several softwares that you can use to input Japanese, for gtk apps(gedit, gnome-terminal, gaim xchat etc) try im-ja http://im-ja.sourceforge.net/
For others(such as Open Office) try kinput2
you'll need to either have Canna or FreeWnn running, at least one of them should be loaded on boot if you chose to install Japanese support, if not you can start them by
/sbin/service canna start
/sbin/service FreeWnn start
You only need one of them, for the purpose of this example i'll use canna.
In order to use im-ja install the RPM whch you can find on the website mentioned above, then run 'im-ja-conf', set the Conversion Engine to Canna, restart your gtk app, then right click, select Input Methods then Japanese. Press F6 and you should be able to start entering Japanese, provided that you are using a proper font under a proper locale setting, which you should if you've selected the language setting in the login screen.
As for kinput2 it should come with Redhat, and might even already be installed (rpm -qa | grep kinput2) if not you should be able to find the RPM in one of the CDs.
In order to use it open up a terminal, type "kinput2 -canna&", open up openoffice and you should be able to use it by pressing "ctrl + o", again provided that you are using a right font and encoding.
One problem with kinput2 is that although it should work in most X apps, the default key combination "ctrl + o" is also used in many gtk apps for open file dialogue, but check the man page for more details on its configuration.