As a land & estate manager in Mythos, I am keen on cleaning out houses that go back on the market, or checking available ones on charm and accuracy. The other day I was renovating a house that supposedly should be ancient, but it had a modern kitchen – with a fridge – that had to be removed, and I thought to myself:
How did ordinary Greek and Roman citizens cook?
This is what I found out:
The traditional and symbolic heart of the home, the kitchen, is inextricably linked with the discovery of cooking food with fire. The use of fire has been known for over half a million years, as indicated by the remains of hearths in a cave in northern China. The “Peking Man” left traces of cooking around the hearth in the charred bones of numerous animals. In the fifth century AD ancient Greeks designed the kitchen as a separate house, and the layout continued in ancient Rome 
Cooking in Rome
Early Roman kitchens were located in the atrium, where smoke from the fire could escape without risk. When the atrium later became used as a living space, the kitchen was relegated to a separate room at the rare of the house. Poorer Romans lived in crowded tenements where fire was a great risk, so communal cooking areas developed for the safe preparation of food. 
They most often lived with their whole family in one room of a small apartment building. So they didn’t have a separate kitchen. Instead, they cooked over a small fire or on a charcoal brazier, either in the courtyard or in their room (if it was raining or very cold). The ones who could afford it, also bought already cooked food in restaurants or from street vendors, of course. 
In early ages of ancient Rome, cooking was done on a stone-lined fireplace, the focus, sometimes built of raised brick into four sides, constructed against a baseboard on which a fire was lit. More common were rectangular and portable focus’, consisting simply of a moveable hearth with stone or bronze feet.
After the development of separate kitchens, the focus began to be used only for religious offerings and for warmth, rather than for cooking. At Pompeii – destroyed in 79 AD – most houses had separate kitchens, most small, but a few large, and a number had no roofs, resembling courtyards more than ordinary rooms; this allowed smoke to ventilate.
Many Roman kitchens had an oven (furnus or fornax), a square or dome-shaped construction of brick or stone. These ovens had a flat floor, often of granite and sometimes lava, which were filled with dry twigs and then lit. On the walls of kitchens were hooks and chains for hanging cooking equipment, including various pots and pans, knives, meat forks, sieves, graters, spits, tongs, cheese-slicers, nutcrackers, jugs for measuring, and pâté moulds. 
Header: Reconstructed Roman kitchen (culina), Museum of London, source wikimedia