Before you apply for a Chinese credit card, discover bank has some kind of agreement with China Unionpay (银联)，if you don't wanna bother, you can use that directly. And they don't charge for international transaction.
The best way to do this is ask for a local Chinese friend’s help, this goes without saying. If someone is not willing to, don't be frustrated. Keep looking, I'm sure someone would like to do it for you.
When you use the online application system, like this one: 新版信用卡网上办卡宣传 be sure to use the Internet Explorer, since that's the most fully supported browser in China. And go to the bank ask the agents there for help is also a good idea, since most of them are just idling around with nothing to do.
To apply for a credit card, you need three kinds of ID cards:
First category: Shows your legal residence.
1. Passport
2. The sticker on the Visa page shows that you can live here legally.
These two are necessary, if you don't what it means, bring your passport and go to the bank and they will help you out.
Second category: Shows where you live. Only one of those below will be sufficient.
* 户口卡（簿）复印件 This is Chinese special, you don't have it.
* 水、电、气最近三期缴费单 Cable bill/water bill/ or gas bills. Three most recent ones.
* 固定电话最近三期缴费单 Phone bill. Three most recent ones.
* 单位开具的集体宿舍证明 Certification provided by your employee about the dormitory you live.
* 房屋租赁合同（协议）Rent contract with the landlord.
* 自有房产证明 Certification of self-owned house.
* 小区物业管理费缴费单据 Receipt of Apartment management fee.
* 街道开具的住址证明 Certificate of your living whereabouts provided by sub-district office.
* 最近二期的信用卡月结单或最近三个月的个人所得税完税证明
Two most recent credit card bills or most recent three months' certificate for paying personal tax.
Third category: Shows you have the financial capacity to pay the credit card company. Only one of those below will be sufficient.
* 政府机构、企业开具的最近三个月的正式工资单或收入证明（需加盖公司章或部门章）
Certificate of income provided by government or enterprise, most recent three months.
* 银行代发工资的存折 /账单复印件（需显示最近三个月薪水入账信息）
Copies of bank account statement book that shows the most recent three months' income
* 最近三个月的个人所得税完税证明复印件
Personal tax payment certificate, You don't have this.
* 社会保险扣缴凭证复印件
Social security payment receipt copy
* 自有房产证明复印件
Self-owned house certificate copy
* 银行定期、活期存款单 /存折复印件
copy of bank account statement book.
* 基金、国债、企业债券购买凭证复印件（需显示购买人姓名、账号和账户余额）
copy of certificate of buying fund, government bond, enterprise bond. (Which must include buyer's name, account number and balance)
* 会员卡类复印件，包括：高尔夫会籍卡，中国移动、中国联通贵宾卡，国航知音白金卡、金卡、银卡会员卡，南航明珠卡金卡、银卡会员卡，东航万里行俱乐部金卡、银卡会员卡（需显示姓名和卡片有效期）等
Copy of membership card, including: Golf membership card, China mobile, China Unicom VIP, the rest are some Airline membership card I don't suppose you have.