In Medan you can find food in shopping centre food courts (where you order from one or more of the stalls and eat in one of the central tables), from a street cart (selling food such as satay, noodle soup, etc.), from a simple cafe/shack known in Indonesian as 'warung', or a Western-style restaurant known either 'rumah makan' or 'restoran'. You can also find Western fast food brands, most notably KFC (and two copies: Texas Chicken, and California Fred Chicken), and McDonalds
You can find good food in all types of eating place, but generally food is better on the street than inside malls.
In Medan the style of food called 'Padang food' is very popular. You will see it from the many dishes of food in the window. When you go into the restaurant a plate of each item is brought to your table. You pay for each plate that you eat, but if you don't eat from the plate, then you don't pay - look but don't touch. There are several Padang chains in Medan, which usually cook the food to a very high standard - these include Garuda and Acc. A larger, busy Padang restaurant is a good sign for quality, but small warungs can be tasty also.
More formal, Western-style restaurants exist in Medan, but they are not really of international standard.
Medan has some good Chinese food. At Jalan Selat Panjang, you can find many choices of Chinese food such as roast duck, dumplings, and others.
One type of food you will see in Medan if you keep your eyes open is 'B2'. This is a polite word, to avoid offending Muslims, for 'babi', or pig. It is BBQed, and served with pork bone soup, and a very spicy sauce made from pig blood and chili. In some areas, where there are more Christians (Karonese and Batak people), most of the whole street is 'B2' warung. In other areas there is none at all.
In the area of central Medan known as 'kampung keling' (India town), you can find Indian warungs serving traditional Indian food.