How was a representative for the Islamic state chosen during the era of the Companions after the death of the Messenger of Allah, peace and blessings be upon him?

The Caliphs were chosen after the Messenger of Allah, peace and blessings be upon him, through consultation among the people of authority and decision-making, or by the preceding Caliph selecting his successor, as Abu Bakr, may Allah be pleased with him, did when he chose Umar, may Allah be pleased with him, after consulting the Companions.