Actually, you don't apply for a work visa as such. It's best to do a little research on the processes and requirements of doing the required paperwork to live in China.

The (very) short and non-detailed version;

 If you've signed and sent a contract along with your supporting documents (degree certificate specifically, also CELTA/TEFL/TESOL certificate), then the next move is your employer's. They will need to send your Foreign Expert Certificate, which you can use to apply for a Z visa at a Chinese embassy or consulate (I believe they'll need to specify which one, ours did). You'll need to do a full health check also in many places, and we had to supply the originals of the documents.

The Z visa indicates that you will be working, but it is NOT a full work visa, it just gives you the time to complete your paperwork in China. The work permit (not visa) and residence permit can be done after you arrive in China, as long as you have entered on a Z visa.

Good luck, and a word of warning. Do not agree to enter China on anything other than a Z visa. Do not agree to come in on a tourist visa and trust them to sort everything out later. You would be working illegally. Any reputable employer should be able to get you a foreign expert certificate, but there are a lot of dodgy potential employers out there, having the proper paperwork helps cover your arse.

I would try hard to visit the website of the Chinese Embassy in your home country.  There, under Work Visa, you will find all requirements for the citizens of your country.  Otherwise, MissA gave you na good answer.

Definitely second both the opinions mentioned above!