This can be a pain if you want to do it right

I usually chose to live with a few compromises in those cases. For example, my last mobile game supported 12 languages, including Chinese, Thai, Russian, Korean, Japanese and other tricky ones.
For this I ended up using the FreeSans font, which already supports a relatively high amount of alphabets and is free to use.
Then I found other free fonts for the languages not included and manually added them to my main font using a font editor tool. In the end I had one big ttf font with support for all my languages.
This way you don't need to do anything extra at all. Just give a string in whatever language to a UILabel and it will take care of it
Pros:
- Everything inside one small ttf file, no multiple big bmp atlases -> good for mobile
- No extra work once it is set up
Cons:
- A lot of one-time setup work
- The font is rather plain looking and not very pretty

Of course for the Asian languages you need to use the simplified versions of their alphabets. They all only have ~50 letters. There should be plenty of fonts out there to use.
Of all the Asian languages Thai is the most tricky one, due to they way the language incorporates spaces and line breaks. Have fun with that

I like the free *** font pages for a good selection of Asian fonts, such as:
http://www.freejapanesefont.com/http://www.freekoreanfont.com/http://www.freechinesefont.com/