You'll be automatically finger printed at any major airport in China.
Those prints are then sent to Interpol.
Just off the plane you'll encounter a kiosk and then again at the actual customs immigration window.
You don't need to be printed as a condition of working in China.
You need a notarized police clearance.
There are a number of agencies licensed to collect prints who then send them onto the FBI for clearance at Clarksburg, VA.
I learned of this service and thought it would be a good idea to share the knowledge, since I had no idea how to get fingerprinted in Japan.
I recently found a fingerprinting service located in Shibuya, Tokyo, called Fingerprint Room Japan. In order to get a visa to teach English in China, I needed fingerprints done for an RCMP background check. They were able to take the fingerprints for me and have all the documents required sent to me in Japan.
They also offer RCMP and FBI background check certificates, as well as printing out digital fingerprints on fingerprint forms.
Fingerprint Room Japan
Hope this helps!