When talking about how an ancient people cooked its foods, it's important to know what ingredients were available to them.
Ancient Greek Pantry Staples
While the foods of ancient Greece were similar to those we eat today, they didn't include many that are standard Greek ingredients today, like tomatoes, peppers, potatoes, and bananas (which arrived from the Americas in the 15th century). The basic foods were cereals, legumes, fruit, fish, game, oil, and wine. Lemons, oranges, eggplant, and rice came later.
The most common cooking methods used by Ancient Greeks were roasting on a spit, boiling, frying, simmering, stewing (over wood-burning fires), grilling, and baking (in wood-burning ovens).
The earliest cooking pots were made of clay, and similar pots (glazed and fired) are still used today in many areas.
Out of necessity because refrigeration was nonexistent, in addition to cooking, ancient Greeks also preserved foods by smoking, drying, salting, and storing in syrups and fat. Foods were often stored with a topping of oil to keep air out.
Who Did the Cooking?
As it seems to be the case in modern times, the men were typically in charge of roasting the meats on spits or over coals, while the women were in charge of boiling foods and baking them in the oven.
When it came time to enjoy the meal, aristocratic people sat or lounged on couches set before low tables laden with food and ate in a communal style.
For the common man and aristocrat alike, utensils were not used. Everything was eaten with the hands. Bread had many purposes at the dinner table—it was used to scoop out thick soups, as a napkin to clean hands, and, when thrown to the floor, used to feed the slaves or dogs.