Basically, you will need a release letter from your old employer, and with that you go to PSB  to apply within 10 days of leaving your old place of employment.  From the new company, you will need the letter of employment, their registration and their authorization to hire foreigners, plus ID photos, your Registration Form of Residence for visitors from local Police, etc.

Please, be aware that you also must go to Work Bureau to transfer the work permit from old employer to new one, and they may or may not require you to renew your FEC and also a new health exam.

No need to freak out, but you have to reach agreement with your old employer, mainly  to get the "Release Letter". The Labour Bureau seems to process the transfer like any application, you may need all the documents again you used for your old work permit. Hand all the stuff in via your new employer with the new contract. In my experience, you can use the residence permit in your passport to leave for a holiday outside China and then re-enter on it for your next job. Would be nice to get confirmation if this is technically 100% legal.

the horror:   please read at http://english.gov.cn/2005-08/29/content_27366.htm in chapter IV, article 20 for your information in the future.

And to anonymous :  besides your Release letter you should make sure you get also from old employer your health certificate (it expires after 6 months of issue), your FEC if they have the original, and if they have your diploma and CV.  You will need those to change your work permit at the Labour Bureau.  At PSB you will need to change your residence permit, since it is also tied to your work place and old work permit.

Technically, if your old employer has not notified the authorities of your departure, it should still be good for leaving and re-entering China.  Buy if they did, you may be allowed to leave, but not to re-enter afterwards.  And if you want to learn what the Law says, please visit the site indicated above.

Thanks a lot for taking the time to get back to me on the issue......!

The process seems very complicated. And my case is more complicated because my "prospective" employer will only hire me if I'm able to extend my residence permit via my current employer, and obviously I can't tell my current employer that i intend to resign and move to another company - and that makes the other required documents such as FEC, release letter, etc difficult to obtain once i quit the old job.....

One of the reasons I wanna transfer to a new company is to grab the chance to live in another city (closer to Beijing)...... But with the residence permit transfer being such a pain of a procedure--- im seriously considering not to transfer to a new company :(

RockistA :  What your new employer wants can not be done.  Maybe he wants it his way because he does not have the permit to hire foreigners, but if you do go and work for him, it will be totally illegal.

You only talk of your residence permit, and I wonder why you do not mention the other factors of the work equation, ie. the work permit, the FEC.  If you change employers. you definitively will need also a new work permit (they are good only for the original place of employment), and depending on local officials, maybe even a new FEC and /or health certificate.  sometimes the whole process is straight forward, and not such pain in you know where.  But sometimes  it could become quite tedious and frustrating.  but you never know until you try it.  

and for Bat 22:  IF OLD EMPLOYER GIVES YOU A BAD REVIEW at PSB, it is not PSB hiring you.  In China, most employers will not talk roses and peaches about former employees who left them for whatever reason.  Yet, many I know do stay in China and get other jobs with better pay, and working conditions.  Just remember, a Release Letter is not a letter of recommendation or about your performance. 

A related question. 

Do you need to resubmit your old CV? If yes, does it need to be identical to the last? It has been two years and do not have the old one. 

Thanks all in advance!