Go to system settings, then "language & region" and use the "plus symbol" in the lower left of the window to add Japanese as an language. Set region and format as you like. These steps might be optional, I didn't try.
Then click to keyboard settings (lower most left big button). Again click the "plus symbol" on the lower left and search for japanese. When you single click to it, choose a layout to your liking. You can inspect the layout with the small button on the lower left depicting a small latin "a". For some reason the Standard layout is not with any japanese symbols.
Also note that in the same main window you got additional "input method settings" as a button on the lower right.
Reboot or logout to make the new keyboard settings work. You should now have a symbol in the top menu bar where you can switch and inspect your configured keyboard languages & layouts.
If you have issues with IBus not being the "default input method" you can follow the instructions from here: How can I use IBus as the default input method?
If you need other layouts like Hiragana you can check out the instructions here: https://askubuntu.com/questions/28669/how-do-i-get-keyboard-to-write-hiragana-instead-of-katakana
If you like the terminal you can always use
sudo dpkg-reconfigure keyboard-configuration for the same stuff.
As a sitenote: I just messed up my own keyboard settings with trying this and for some reason I always need two configured languages for the keyboard so it's working properly.