What is the fastest method to type Chinese using a computer?
Theoretically the fastest method seems to be 速录.


  亚伟速录常用于会议的听打，最快可达500字/分。 


Apparently you can type five hundred characters a min. It is basically a type of shorthand used by stenographers. The learning curve is, obviously, going to be quite high though, as you would expect of stenography.



There's a short article saved here from China Daily that talks about it a little if you're interested.


  For decades, Tang Yawei's name has been synonymous with stenography in China.
  In the 1930s he developed a standardized Chinese shorthand method, Yawei Chinese Shorthand, which is now widely used, especially by journalists and professional stenos.
  
  Then in 1994, at the age of 79, he invented the Yawei Chinese steno machine, allowing stenos to record up to 200 words per minute - about 75 percent faster than shorthand while eliminating the need to transcribe notes.