What is the procedure to get the employment permit if I change the employer?

Your new employer should handle it for you.
Prepare following documents:
1. Release letter stamped by your present company;
2. New company's business license;
3. A copy of Certificate of Approval (if the new company is a WOFE); A copy of the Social Insurance Registration certificate (if the new company is a Chinese company);
4. Application letter written by the new company and addressed to Labor and Social Security Bureau, explaining why they would like to employ you;
5. Resume Written by yourself (in Chinese);
6. A copy of degree certificate (needs to be translated as well)
7. A copy of labor contract with the new company;
8. Employment Registration Form of Foreign Employees;
9. Visa and residence permit application form;
10. Two 2-inch photos;
11. original Passport;
12. Your old Alien Employment Permit;
13. A copy of Temporary Form of Residence Permit.