Archeologists aren't sure if iron smelting was invented once and then spread by word of mouth, or if it was invented in several different places independently. It was done in India by 1200 BC, in both Greece and China by 900 BC, and in Nigeria by 550 BC. The earliest iron made by humans was wrought iron.
Iron smelting requires a temperature of at least 800°C. A furnace is used instead of an open fire because with a furnace the fire burns hotter, the temperature is more consistent and predictable, and less fuel is used.
The furnace used by the earliest iron workers was probably a simple cylinder of clay or brick, about a meter high, wider at the base, open at the top and with a small opening near the bottom to let air in. The furnace is packed full of charcoal and iron ore, and the charcoal is set on fire. Since hot air naturally rises, air rushes through the furnace, entering at the bottom and exiting at the top. A bellows (air pump) might be used to drive air through the furnace to make the fire hotter. Inside the furnace a chemical reaction takes place: the iron ore, which is mostly iron oxides, is converted to iron.
When the hot iron is taken out of the furnace it is glowing red and has a soft, spongy texture; this iron is called a bloom, and the furnace that produces it is sometimes called a bloomery furnace. The bloom is forged, or repeatedly over with a hammer, to drive out slag (impurities). And the metal is repeatedly beaten flat and then folded over, to 'mix' it, giving it the same consistency and characteristics throughout. The final result is a lump of metal ready to be re-forged by a blacksmith to make useful things.