Cyrillic/Russian Characters in Chat

I can see Cyrillic/Russian characters perfectly fine in chat.
When I switch my keyboard input to type these characters, however, I am only able to print out Latinized characters with modifiers over them.
How do I set up my client so that I am able to type with Cyrillic/Russian characters?
...and switch between Cyrillic/Russian and Latin input?
When I switch my keyboard input to type these characters, however, I am only able to print out Latinized characters with modifiers over them.
How do I set up my client so that I am able to type with Cyrillic/Russian characters?
...and switch between Cyrillic/Russian and Latin input?