Is it easy for a foreigner to get study or work permission to China?

If you are highly educated, it will be relatively easier for you to get work permission to China. First, you need to get a job offer from an employee who holds the Alien Employment License. Only this kind of emplyee can provide you with Work Permit and "Invitation Letter of Duly Authorized Unit" or "Confirmation Letter of Invitation", with which you can apply for a work visa from the China embassy.
If you want to study in China, you must first get enrolled by a China school, the school will then provide you with Enrollment Letter and more importantly JW201 or JW202 issued by the China authority, with which you can apply for a student visa.