Research is key. You need to maximize research from the very beginning. For example, when you finish researching the Calendar, you want to have a lot of workers to get all the Plantation resources online as quick as possible. Not only do these greatly contribute to gross commerce, they bring happiness as well which allows much bigger cities. Even better, trade them with Europeans. I'd recommend having at least 10 or 12 at that point, which is not too hard considering most Chinese cities aren't exceptionally good at building anything else. Towns and mines are the standard improvements on all tiles without resources. That should get the domestic economy going. I should also point out that I didn't switch civics for a very long time, the reasoning being upkeep. One of the key differences between game 2 (prosperous) and 3 (failure) was civic upkeep, multiplied by a massive inflation in both. For example, Organized religion, which is usually one of my favourites, costs a huge pile of money each turn. Better stay at something cheap or not waste the turn of anarchy at all.
Also, try to make sure the trade routes go to Europe. India is very nice for early international trade, but compared to what Rome has to offer it's nothing. Sometimes there's a barbarian blocking your trade route, but you have to make sure to get European trade routes most of the time.
That's basically it. Always search for ways to increase commerce and science, preferably in that order. Try to keep upkeep to a minimum. What I learned from the 3rd game is that you actually do have some influence on that apart from the basic Courthouse. It's such a pity when you're stuck with only 5 cities and still have to set the research bar to 40%. China has a huge potential, I got the Triumphal Arch with all Medieval techs already discovered in 1140 AD and I'm by no means a great player.
Wait until the 1.12 release, replay and post your victory in the new thread which will be opened after the release. I should probably add this to the OP.I'm sorry to say it but to avoid confusion with the new difficulty levels, games on SVN revisions starting with 757 are not excepted. However, non SVN (1.11) and SVN 756 and before games are still excepted. I hope 1.12 will be released soon.
@ Sovietof17: I chose to settle all of them with the exception of Pyonyang. However, if Korea built another city I'd have razed that and built Pyonyang anyway. Of course you can settle for Seoul which is decent, but I dislike suboptimal city placement, even if it means that I have to raze some.
@ ales: I'm familiar with the concept, in fact, I was the one who originally came up with it. Therefore, I'd argue that it's not just any 'in' goal, but more generally that you have achieved all three goals but you simply have to wait until some point where the goal is triggered. In this case, I'd argue that having all the prerequisites for the 3rd goal (32 turns of Golden Age) ready but having to wait for that third goal to trigger is valid for a virtual victory. Of course, it could be said that it's simply 8 turns after you start the 4th, but in some cases it is not, like the one in mine where 3 and 4 overlapped. Therefore, I think it could be added, but it's not really important to me so don't worry.