China has a long vegetarian tradition due to Buddhism, there was quite a bunch of vegetarians in China a thousand years ago. Things have changed, however, for the worse. Nowadays vegetarianism is largely unknown except for Buddhist monks. The common question to vegetarians would be if they eat onions -- this surprised me at first, but the Buddhists don't and ethical veg*nism isn't really known here. However, things aren't quite as gloomy as that may sound, for the tradition in cooking persists.
The big cities in China have a number of vegetarian restaurants... about one per million inhabitants, but nonetheless. They can usually be found near or even inside temples, or one can look up where they are from the internet, a list is maintained
here by the International Vegetarian Club of Beijing -- but only in Chinese. I'll translate at least some of it here later. They're not completely vegan, but some do not use eggs at all and Chinese cooking generally doesn't use dairy, so most of the things served are suitable for vegans.
As for the regular restaurants, things are more difficult. Tofu dishes often have meat in them, and vegetables may be prepared in meat broth. These are easy to prepare differently though, and most restaurants are willing to do so when asked -- in Chinese. Language skills are essential here. I haven't tested the reception of the Vegan Passport, it might be of use. Generally speaking the south is easier than the north and the east easier than the west... and the big cities much easier than small towns.
The food you get in these is generally quite tasty, although rich in oil. This is the home of tofu, so that is plentiful. The vegetarian restaurants have a plethora of mock meat and fish dishes, to the degree that one starts wondering what is the point. The most ridiculous thing is the vegetarian "pork", where they even add a fake layer of fat on top! Why not imitate better than reality?
The universal key to eating vegan, however, is cooking vegan. The shops and markets sell nearly every kind of vegetable you may want, and tofu is indeed aplenty. They have all sorts of fake meat things in many supermarkets also, a thing that makes you wonder if there is some sort of hidden vegetarianism under the covers. But if you're into cooking Western style vegan food, do note that they generally don't have ovens in China, and that makes things a lot more difficult. Some of your usual ingredients may not be around either, or may be hard to find, especially if you don't speak the language. The big international supermarket chains like Carrefour do have a lot of Western foodstuffs around.
Overall, veganism in China isn't too bad at all, but be prepared for things going wrong sometimes as people won't always understand and they do make mistakes. There can be positive surprises too. Like when I was on a train from Shanghai to Beijing and they served us dinner, I refused the food by telling the train attendant I was vegetarian. To my utter surprise she returned a few minutes later with a completely vegan meal that inspired the meat-eaters in my cabin to ask her "Why does he get better food than us?". Her reply kept me smiling for days: "Because he's vegetarian." :-)