Almost the same as anywhere else: treat her with kindness and respect, don't assume anything, and be a gentleman.
Other tips:
Perhaps I'm not the best person to reply- I only grew up partially in China, though I maintain close ties with her. Neither have I dated Chinese women, being straight and all- though I have dated foreigners while in China.
So among the mistakes that these men have made to turn me off (not that I was an absolute angel myself), perhaps these might help-
At the end of the day, as long as you see them and treat them as people and not labels or concepts, it's all good. Be prepared for stares and jibes, though- but eventually you get used to that, too.
We're all just co-people, as Ron Burgundy might say. :) Good luck.
If you're living in China and thinking about starting a relationship while you're there, one of the best things you can do for yourself to better your chances is learning Chinese.
Something that always leaves an impression on people is you taking an interest in them. So if you want to impress a Chinese girl, you should consider studying up on Chinese language and culture. Depending on where you're from, there could be a lot of cultural differences that could complicate and even threaten your relationship if you aren't both on the same page. Plus wouldn't it be sweet if you could speak to her parents or grandparents in their native language, even if she is able to speak English with you?
eChineseLearning is an online Chinese tutor program over Skype, and they've actually got a course designed with Sinophiles in mind--Chinese Lessons For Dating!
According to their website, "This Mandarin Chinese course is designed for those who are or intend to be in serious relationships and are interested in learning to express their true feelings and emotions in Chinese. All lessons in this course are based on real dating scenarios.
Through Chinese lessons for dating, you will learn the most useful words, phrases and sentences on various topics involving love and romance (selected list):
Sounds like a great way to learn the kind of Chinese you'd want to know if you wanted to start a relationship with a Chinese girl. Much more helpful than a textbook that's gonna spend three months teaching you how to order drinks in a restaurant and shop for food at a grocery store.