Q. How did ancient Greek people make their food? What did they eat?

Here is a quick summary from The Spruce about what the Ancient Greeks ate and how they cooked their food.  For more information, check out the Links that i have provided with this answer. (NOTE: the information originally provided with the FAQ has been added to):

The foods of ancient Greece were similar to foods we eat today, but did not include many that have become important parts of modern Greek cooking. For example, tomatoes, peppers, potatoes, and bananas didn't arrive in Greece until after the discovery of the Americas in the 15th century, because that's where those foods originated. Lemons, oranges, eggplant, and rice also arrived later. But the ancient Greeks enjoyed a varied diet. Vegetables, legumes, and fruit were the mainstay, and fish was a favorite. Hunting brought game to the menu.

The most common cooking methods used by Ancient Greeks were boiling, frying, simmering and stewing (over wood-burning fires), grilling, and baking (in wood burning ovens).

The earliest pots were made of clay, and similar pots (glazed and fired) are still used today in many areas.

In addition to cooking, they also preserved foods by smoking, drying, salting, and preserving in syrups and fat. Foods were often stored with a topping of oil to keep air out.

[https://www.thespruce.com/what-did-the-ancient-greeks-eat-1706101]