I work exclusively as a private tutor myself (I grew totally disillusioned with the EFL industry in China) and (shameless plug) I have written an article on the subject on this site (
Ed's note: see Freelance English Teaching in China).
I think many language centres are even unaware of the legal situation here, many advertise saying they want part-time teachers who already have their work visa from another school, whether that be a university or otherwise, thinking that clears the teachers to work legally for their institution when--as stated by Ken and Dr Greg--that is not correct.
I openly admit I have worked in this manner since November 2009 on L-visas alone after three different schools promised to get me the proper paperwork and reneged on that promise. Please note I am not advising anyone else to do the same, quite the contrary actually. I have to go to Hong Kong every 2 months to renew my visa just so I don't overstay. The situation is permanently volatile especially during times such as now when there is a sporadic crackdown due to Shenzhen hosting the Universiade Games. However, as a purely practical manner, I feel it is highly unlikely you will get caught tutoring as most of the time you are teaching in your students home or place of work. This is the reason why in my article I stress you should not use your house as a place of business to conduct your classes.
My advice for any newbie's looking to move to China to teach EFL is this: Get a job at a university or a public school (not a training centre for reasons outlined in my article) in preferably an affluent part of China. Don't worry too much about the salary, find a position with good perks such as holidays fully paid, 12 months pay not contingent on renewal, good travel allowance, medical insurance and crucially an off-campus apartment or housing allowance (best option). This takes care of visa and housing, and paid holidays. Now fill up your considerable free time with choice private classes and aggressively market yourself as a private tutor charging an absolute minimum of 150RMB an hour in 2nd and 3rd tier cities and 200RMB an hour in first tier cities. You should soon have an income in the 12000-18000RMB a month range. You can't count on this right away but with a bit of effort it is attainable.
If you want to make money teaching in China, tutoring and freelance work is usually where it comes from.