The process is a little different for each person and each country. The biggest part is a three step authentication for your diploma, police check (and TEFL certificate for a number of the areas).
It is a little confusing but basically before the Chinese embassy (often done through the visa office) will authenticate the documents they need the documents notarized by the state/province/county, and before the state/province/county will notarize/authenticate the documents they need to be authenticated locally.
There are companies ($) that can help with the process as well depending on how far teachers are from the services they need.
Please see here for the visa requirements/process.