The most important thing to realize about food back then is that most people never got enough to eat, and many people starved to death. Food was expensive, and they didn't have food stamps or anything like that.
When people could get food, the food people ate varied a good deal from time to time and from place to place. So you'll need to read about each time and place separately. There are some things all these times and places had in common, though.
First, one reason food was so expensive was that there
was no refrigeration or freezers. It was very hard to keep food from
going bad. People did a lot of different things to preserve food. They
dried fruit to make raisins, prunes, dried peas, and dried apples. They
pickled vegetables, meat, and fish
in brine (salty water) to make pickles and garum, a fermented
fish sauce. They fermented grape juice and apple juice and barley to
turn them into wine and cider and beer.
They made yogurt and cheese. They
smoked meat from pigs to make ham
and bacon. Honey also acts as a good preservative.
(Suggestion for food projects)
Second, because it was so hard to carry things from one place to another without canals or trains or trucks, people usually could only eat what was available in their area at that time of year. If there was a shortage of food because of bad weather or crop diseases, people starved. Even in a good year, it was impossible to get fresh vegetables in the wintertime!
Third, before Christopher Columbus came to America in 1492 AD, and even for some time after that, many of the foods we eat today were not known in Europe, Africa, or Western Asia. They had no potatoes, no tomatoes, no corn-on-the-cob (maize). Europeans also had not yet gotten rice or citrus fruits (lemons and oranges) from India. Indian spices like cinnamon and pepper were available in Europe, but they were very expensive.
Western Asian food
Islamic period food
To find out more about food in antiquity and in the middle ages, check out these books from Amazon.com or from your library:
Food, by Fiona MacDonald and others (2001). For kids, facts about food from all over the world. A little preachy.
Food and Society in Classical Antiquity, by Peter Garnsey (1999). Garnsey has written a lot about ancient food, and is an expert, but he writes very clearly.
Food in Antiquity: A Survey of the Diet of Early Peoples, by Don and Patricia Brothwell (1998). Pretty specialized, but the book tells you where foods came from, and how they got to other places, and what people ate in antiquity. Not just Europe, either!
Food: A Culinary History from Antiquity to the Present, by Jean Louis Flandrin, Massimo Montanari, Albert Sonnenfeld. (1996). Hard going because it is translated from French, but Flandrin was one of the world's great food historians.