Poor people who lived near the Mediterranean Sea had to eat food that would grow in very dry areas, with light and not very fertile soil. Mostly they ate what archaeologists call the "Mediterranean triad" or three things: wheat and barley (made into beer or porridge or flatbread or soup), olive oil (soaked into the bread, or on vegetables), and grapes (made into wine, vinegar or raisins so they would keep). People also grew beans and a lot of different kinds of vegetables and fruit.
Some foods that were especially common were
onions, carrots, garlic, and cabbages
honey (they didn't have sugar)
herbs like dill, thyme, oregano, basil, and mint
nuts, especially walnuts and chestnuts and acorns
cucumbers (they didn't have tomatoes)
eggs (from chickens and from geese and ducks)
yogurt and cheese, mostly from goats and sheep
mutton (sheep meat), goat meat, and pork and ham
and bacon, chicken, goose and duck, and fish, especially tuna. Oh, and snails - people raised them in special snail gardens, with little box hedges for them to crawl on.
One item that was very popular was a fermented fish sauce: you can find something like it today in the Thai foods section of the grocery store. Or Worchestershire sauce is probably similar too. They used it on everything, the way a lot of people use ketchup today.
Some things you might make to see how these Romans ate:
oatmeal (or barley porridge if you really want to do it right, or cream of wheat)
pita bread with yogurt or feta cheese
pita bread with falafel (ground chickpeas)
pizza crust with olive oil poured on it, with feta cheese, thyme, onions and/or garlic, baked (remember, no tomatoes!)
barley soup with onions and carrots
lentil soup with onions and carrots (try mixing some yogurt in)
split pea soup
yogurt mixed with chopped cucumbers
and garlic (tsatsiki)
cucumbers with oil and vinegar (actually, the Romans ate them with honey)
roasted leg of lamb with mint sauce
For some Roman recipes, check out these books from Amazon.com or from your library:
Spend the Day in Ancient Rome: Projects and Activities that Bring the Past to Life, Ages 8-12 by Linda Honan (1998). With recipes for a whole Roman feast, for kids.
Roman Cookery: Ancient Recipes for Modern Kitchens, by Mark Grant (1999). Recipes for things ordinary Roman people ate, not the fancy stuff.
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!
And check out the great bibliography of food books and articles that Sue Alcock has posted.