Ren, you are taking a bit of a risk. For me, there have been experiences where the school will send you to Hong Kong to get a legitimate Z Visa after you arrive in China, and being that you would be going on an L Visa they are required by law to do this or else you would technically be working illegally.

The best(and most professional) way to carry this out is ask your school to send a Letter of Invitation (this is the offical name of the document)to you, go and fill out a Health Check Form which can be downloaded from the Chinese Consulate website and then spend some money at a local clinic in your home country getting a physical and get the doctor doing it to fill the form out, obtain about three 2 inch passport photos, make a copy of the front page which is the picture page of your passport, and bring all of these things to the Chinese Consulate and fill out the Visa Application Form there(you may also download it as well from their website). Now I am not sure about this but your school may also need to send you a copy of their Organization Code Certificate (Kind of like a Business I.D. number that a corporation would have) called a "Zu Zhi Ji Gou Dai Ma Zheng". You will need all of these docuements to get that Z Visa, which from my personal experience carried a 30 day period of validity which means your school will need to provide you with a Resident Permit within 30 days after you arrive in China. This Resident Permit is a sticker that is also placed inside your passport allotting you the time in which you can stay in China, usually for the length of the contract that you sign with the school, maybe a little bit shorter though (so the school can try and get away with not paying your flight allowance since you didn't work there technically for 1 whole year).

If you decide to do the L Visa route, be sure to have enough money to get a Health Check at the local health clinic wherever you go in China. They will give you a small orange booklet called the Certificate of Health Examination. From there your school is responsible for providing the necessary documents stated in the previous paragraph except the Health Check Form in order for you to go to Hong Kong and obtain the Z Visa.

Now some schools will do things the illegal way by constantly extending your L Visa by 90 days every time your L Visa runs out of time at the local Police Station. If you are not asked to get a health check or do a visa run then you can expect that this will be the way for the school to keep you around. While this is convenient, it is also illegal. You will risk being detained as well as blacklisted from working in China if you choose to go this route. Whatever you do, please realize that you cannot be too careful when dealing with business as it's done the Chinese way. Good luck.