First I go to the Language Support window. Either search (press Super/Windows, then type) for "Language Support" and go there directly, or search for "Region & Language", go there, then click "Manage Installed Languages".

There I click Install / Remove Languages ..., check the Chinese I want, then click Apply.

Then I add the packages for the input methods I want, either using the command line (apt install) or the Ubuntu Software application:

• Chinese Quick: ibus-table-quick-classic
• Chinese Pinyin: ibus-libpinyin
• Chinese (Cantonese) Jyutping: ibus-table-jyutping

Bonus input method:

• Unicode emoji: ibus-typing-booster

Now for each user that wants an input method, I search for and go to Region & Language. At the bottom of the Input Sources section I click the plus button. The different input methods are found by clicking down into different sublists. Click the right choice, then Add:

• Chinese Quick: Chinese -> Chinese (QuickClassic)
• Chinese Pinyin: ⋮ -> Other -> Chinese (Intelligent Pinyin)
• Chinese (Cantonese) Jyutping: Chinese -> Chinese (Jyutping)
• Unicode emoji: ⋮ -> Other -> Other (Typing Booster)
• EurKEY: English (United States) -> EurKEY (US based layout with European letters)

The EurKEY layout is part of the standard English language support in Ubuntu.

Finally, to enable unicode color emoji as completion suggestions, switch to the Typing Booster mode by pressing Super/Windows+Space repeatedly until you see the rocket in your notification area. Click the rocket -> Unicode symbols and emoji predictions -> On.

I owe you a followup episode once I figure out how to make this work for Guix applications running inside Ubuntu.

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This episode was based on a Fediverse thread:
https://libranet.de/display/0b6b25a8-6760-517c-52c9-654926232346

References for your further study:

• IBus is an input method protocol for the GNU/Linux desktop. Other protocols supported are XIM, SCIM, fcitx and uim. You have to choose one of these to use for all your input methods, but the most common input methods exist at least for IBus and the first three of the rest, so this is not as much a limitation as it sounds like.
• Quick is a simplification of the Cangjie input method. Cangjie assigns radicals, character components, to 24 keys on the alphabetic keyboard, and you combine these into a character. In Quick you combine two and then choose a completion from a list.
• Pinyin is a romanization, a Latin alphabetic spelling, for Standard Chinese (Mandarin).
• Jyutping is one of many romanizations for Cantonese.
• Guix is a GNU/Linux OS and also a package manager that can be installed and coexist with the GNU/Linux OS you already have, allowing you to mix and match programs from both sources. See also hpr2198 and hpr2308.