If you are over 18 and have a valid driver's license of another country then you will most likely only need to complete a written (computerized) test to obtain a 6 year Chinese driver's license for a minimal fee.
You should go to the Shanghai Driver's Licensing Centre
Address: No. 179, Qinchun Road, Minhang District.
Office hours: 9:00 a.m. - 5:30 p.m. on Monday-Thursday; 
                   9:00 a.m. - 4:00 p.m. on Friday
Tel: 021-64987070

Essentials:

• Bring someone with you who can write Chinese
• Take photographs at the center
• Collect a standard application form and complete the form in Chinese script
• Have a medical examination
• Have your foreign driver's license translated into Chinese at an authorized translation service center
• Take the papers needed (pictures, passport, foreign driver's license, and Chinese translated license) back to a reception counter
• Make arrangements to take the written test

If all of these steps are followed without incident, you may receive your Chinese driver's license within 5 days after passing the test and paying the fees.

Fees:

• Service charge: 5RMB
• License fee: 10RMB
• Written test: 40RMB (if you pass the first time)