The two major grocery store chains are Carrefour and Tesco. Think of them as Wal-Mart plus a dash of target. These chains will have most of everything you need from clothing, electronics, groceries, toiletries, and everything in between. The imported food will be limited and often rather pricey. There are plenty of local grocery stores and fruit markets located in every city. Most labels will include a Chinese and English translation for general staples.
Online grocers are becoming very popular and are often the best sources for imported food (fresh or frozen) as well as alcohol.