Most metals are found in the Earth's crust as compounds in rocks called ores, often as oxides. Carbon sits in the reactivity series between aluminium and zinc. A more reactive element can take oxygen from a less reactive one, so carbon can remove the oxygen from the oxides of metals that are less reactive than carbon, such as zinc, iron and copper. Removing oxygen from a compound is called reduction, so the metal oxide is reduced. Metals more reactive than carbon, such as aluminium, cannot be extracted this way and are extracted by electrolysis instead.
Iron is extracted in a blast furnace. Carbon burns to make carbon monoxide, which reduces iron(III) oxide to molten iron: Fe2O3 + 3CO → 2Fe + 3CO2. The other product is carbon dioxide.
Copper is a non-ferrous metal, which means it is not iron or a metal based on iron. Copper oxide can be heated with carbon: 2CuO + C → 2Cu + CO2. The carbon gains oxygen, so it is oxidised, while the copper oxide loses oxygen. Heating to high temperatures needs a lot of fuel, so industrial extraction has an energy cost.