This is almost always done by the employer...I think it ranges from difficult to impossible to get one of these on your own and without a specific job lined up.

The employer provides the local Labor Bureau some proof that you have desirable knowledge or abilities- such as a university diploma, a teaching certificate, certification in a specific skill, etc.- plus copies of your travel documents and of course good old-fashioned mountains of Chinese paperwork.

Naps are taken, tea is consumed...and a few weeks later a small brown book is excreted that you can then use to go obtain your Residence Permit.

This, by the way, is why schools are so insistent upon a university diploma. It has little to do with on-the-job qualifications and much to do with getting your FEC.