Following advice given here, I seem to be further along. Also, switching to KDE seems to have helped as well.
Now, when I open certain applications, mainly FireFox and OpenOffice, I get a small "Input Switcher" window. It has only a drop down menu on it, and if I click on the drop down, I see "Japanese" as an input option. But, if I select that, then nothing really happens. Typing in the application still happens in English.
If I click on the "system-switch-im" icon in the top panel, I get a window which allows me to select an "Input Method System". I can choose "iiimf" or Advanced Settings. Under Advanced Settings, Japanese is listed. If I go into advanced settings and select Japanese, I'm further presented with different input methods. Can't quite figure out what the difference is between them, though, as selecting any of them doesn't seem to do anything.
Dave