I have LO on Ubuntu as a VM on a Mac. How can I write and read Japanese characters?
To read japanese, you just have to install a font that contains the necessary characters (UmePlus fonts are easy to read - also the Epson fonts are nice (although not packaged)).
To be able to write japanese, you need to install an Input Method Editor (IME). I personally use ibus with anthy.
http://packages.ubuntu.com/search?keywords=umeplus
http://packages.ubuntu.com/search?suite=default§ion=all&arch=any&searchon=names&keywords=ibus+gtk
http://packages.ubuntu.com/search?keywords=ibus-anthy
But the only part that is related to LibreOffice is how to use the IME in LO - if you use ibus-gtk and the gtk-integration package, then it should work already out of the box. (default shortcut to activate/disable IME is +, amongst others)
Menu/Tools/Options/Language Settings/Languages - Enhanced language support - Enabled for Asian languages