Connections
China uses connections and networks in the same way we use the Yellow Pages and Google - they're where you start when you need something done.
As a new foreign teacher, you start with a completely blank sheet as far as guanxi (connections, relationships) goes. All is not lost though, as you do have the means to start scribbling on that blank sheet. It won't be long before you are asked for favours of some sort - attend a photo-shoot for a new marketing brochure, or spend a Saturday helping the principal's cousin prepare for a visa interview, or spend all of your weekends and two evenings a week teaching the head of the English department's kitten to juggle - anything is possible.
When you agree to help out with something like this, you become part of the great guanxi network, which stretches unbroken across China. For example, you agree to teach some local VIPS two evenings a week for extra money, even though you are very reluctant. The VIPs are grateful to the school for this favour, and one of them works for the PSB and offers to smooth the path of any visa applications that come his way. Mutual back-scratching like this is common, all carried out in the currency of favours, gifts and banquets.
The tricky part is getting something back. First of all you need to make sure the people you do favours for can reciprocate - sure, giving your students extra tuition might make you feel warm inside - but is it actually going to get the heating fixed? Unlikely. You'll need to 'accidentally' drop by the little room where the guys who fix things live after 'coincidentally' buying some cigarettes and beer to get that done.
Until you're a bit more confident in manipulating all this, it doesn't hurt to be relatively direct. I once told my waiban that I would be very interested to think about the extra teaching the school wanted me to do, but I do all my best thinking in the shower in the morning, and as it happened my hot water tank appeared to be broken, thus robbing me of valuable thinking time and leaving me unable to consider his undoubtably generous offer. The hot water tank was fixed within 24 hours (and stayed that way for about as long, but that wasn't his fault)
It can all seem somewhat corrupt, of course - it's easy to want to stamp your foot and say 'but it's your JOB to do it'. That's nowhere near as much fun though.
Corruption aside, the easiest way to build up your balance sheet is simply to be friendly and have time for people. I found the guards on the gate at one school wouldn't let my taxi through when I came home late, so I had to walk through the campus. I started chatting to them when I walked past on my way out, and soon enough they were waving taxis through. A friendly and helpful attitude works wonders.