Gnome 3.x based desktops
See http://blog.fedora-fr.org/bochecha/post/2012/09/Inputting-Hong-Kong-Chinese-with-GNOME-3.6
Current Gnome 2.x based desktops
Entering characters from outside the Latin alphabet on Linux desktops
First, open the "Input Method" tool
Select "Use iBus"
Click on the "Select an input method" chooser
For this example, we'll use Chinese Pinyin
We need to "Add" the select method and close the tool
When we want to input non-Latin text, click on the top toolbar to change the input. Note that you must be in a text input area to change this.