A quick guide to Chinese cuisine:

Northeastern food (Jilin, Heilongjiang Provinces) is the most similar to the U.S., with more beef, potatoes, stews, corn, and bread. Ethnic Korean restaurants serving dog meat are common in Jilin.
Guangdong is famous for dim sum, pastries with hot dogs in the middle, and for eating all kinds of weird animals.
Sichuan, Hunan, Hubei food is usually fiery hot with peppers (e.g. kung pao chicken -- gongbaoji)
Shanghai food tends to be sweeter and milder
Chongqing hot pot is popular in Beijing and elsewhere. It can be quite hot but fun
Xian has a very cool street where you can eat all kinds of Muslim foods, which are heavy on mutton and beef (no pork or beer). There are muslim restaurants and muslim neighborhoods in Beijing and most other northern cities. You can find vendors selling mutton kebabs on the street everywhere.
Shandong food tends to be rather bland.
Coastal cities will serve you all kinds of seafood, including creatures you didn't know existed.

Buying Food

Traditionally, fresh vegetables and meat are bought in street markets. On one side is a cement counter with numbered stalls.In the center, farmers park their carts and sell vegetables. The market is divided into sections: meats, grain, vegetables, fruit. There may or may not be signs to tell you the price. Sometimes you might have to bargain over prices but don't bargain for food prices until you have enough experience to know what the correct price should be. Food in street markets is usually very cheap.

Duoshao Qian?

After you've determined the price, you tell the seller how much you want, usually how many 'jin,' which is a Chinese weight measure close to a pound (half kilogram). 'Jin' are divided into 10 'liang.' The vendor will weigh out your selection on a scale. Some will have a mechanical scale. The more down-scale farmers have a wooden stick with a weight on one end and a tray on the other end. They hold the stick by a string, then move the string along the stick until it balances. The position on the stick is marked with little dots that indicate the weight. They would always show me the dots and I would nod my head knowingly, having no idea what the dots actually meant. They would often try to load us up with about 10 pounds of carrots or green peppers. Ways of cheating, besides having fixed scales, include sneaking rotten stuff in the bottom of the pile. In 1991 we had to bring your own bags, but now vendors usually provide them.

Supermarkets. Chinese cities now have western-style supermarket chains, very similar to Chinese supermarkets you can find in most large U.S. cities now. They are more expensive, however. In some of the richer cities you can find foreign "hypermarket" stores, including Carrefour and Wal-Mart. Convenience stores, including 7-11, are also becoming popular. Supermarkets are usually clean and have good quality products, but they're more expensive than street markets.

Restaurants. China has tons of restaurants at widely varying prices. You can get a decent meal at a food court or cheap restaurant for 16 yuan (less than $2). Restaurants usually have an open area with lots of tables as we're used to, but they also have private rooms in the back. They always have a round table. The dishes are placed on a "lazy susan" in the middle of the table so everybody can reach them. Each person gets a small plate in front of them. Then each person takes whatever they want using chopsticks or a spoon.

There is usually beer to drink, but you can ask for coke, sprite, juice, soymilk, yoghurt, etc. In a formal banquet everyone has to give a toast, followed by a "gan bei" (dry glass) where everyone must empty their glasses.

Fast food is popular now. McDonalds and Kentucky Fried Chicken are in most major cities. You can also find A&W American Food, California Noodle King, Pizza Hut, and TGI Fridays.