unicode input in X apps: how to?

[James Miller <jamtat@mailsnare.net>]

I can't seem to puzzle out how to input unicode into X apps: specifically,
I need to do this in OpenOffice.org.  My Windows "friends" all have
keyboard switching programs that allow them to select different unicode
fonts so that they can write their friends in Urdu, Byelorussian and
Mandarin.  Meanwhile, I sit here with my "superior" Debian OS unable to
match their facile success.  Of course I can enter a character at a time
using the character map feature of OOo.  But I'd like to just be able to
type away at the keyboard in Russian, Greek or Tagalog.  So, is there some
way to accomplish this under Debian?  Do I need some sort of keyboard
switching program like those awful Redmond-worshippers use?  Is it a more
manual process under Debian or Linux in general?  In spite of having read
some things on unicode, I still don't have a very clear idea of what to
do.  Can anyone offer help, point to links, or make other such helpful
gestures?  I know I can use old-fashioned "dedicated" (my term)  fonts to
make foreign languages appear in OOo.  But I'm trying to keep with the
times and use the latest and greatest unicode everyone keeps raving about.
Help, please?

Thanks, James