How long does it take to get a work visa, and once you have a work visa is it easy to transfer to other companies or other types of work?
I presume the ESL company who you work for sponsored your visa??
Also whats the food shopping like there, I've read that china has a lot of problems with counterfeit food and contamination.
The work visa can be obtained before you even come here. You can interview on Skype and get offered a job. I'm not sure if you're American, but if you are, you need to apply for the visa before you leave the States. Other countries are a little different.
Otherwise, you can come on a tourist visa and, once hired, the company applies for the work visa for you.
In China, the work visa is obtained through a Chinese employer. Once they get you a visa, however, you will be under contract for that company (usually a year at a time). You may be able to moonlight, but they probably will want you to be working for them.