Chinese input is non-existence out-of-box from Ubuntu (and up to 20.04 so far). More work is required to setup Chinese input support. While there are multiple variances out there, Chinese Intelligent Pinyin works best for me.
To install Chinese Intelligent Pinyin, search "ibus-libpinyin" online. Basically, update ibus then install ibus-pibpinyin.
sudo apt-get install -y ibus-libpinyin
Perform a reboot. Note, there is a way to refresh without a reboot but reboot is easier.
Then go to Settings > Language and Region, under Input Sources, click + then Other. Select "Chinese (Intelligent Pinyin)" from the list. Note, it is not "Chinese" in the list as it basically does nothing.