Hi @Nick,
The way to install packages is by using a terminal.
Launch a terminal, called tilix
In that terminal, when you are logged in as the current user, the convention is to describe the line by starting with $
When you are logged in as the-super-user-that-has-all-rights, also called root, we describe those lines with a #
As an example, if you read "type echo 'test'", we can show the command and output as follows:
$ echo 'test'
test
So, when opening the terminal, you need to get the root privileges to be allowed to install anything.
$ su -
Password: <you type in your password and nothing appears>
#
From there on, you can use the apt command to browse packages. Simply typing apt will display the help. Spend a bit of time on that help to learn more 
You can search for what @kajika told you about:
# apt search mozc
You can install the needed package as follows:
# apt install ibus-mozc
Now you should have the package installed. I’m not a specialist regarding either ibus nor japanese input. Probably @kajika can tell you more about it