What did Iron Age Kingdoms do to control huge amounts of land distant from thier capitols?
Iron age rulers used many different techniques for establishing control over far-flung territories.
In Rome, they used a combination of military and civil control to keep their imperial provinces together. The Romans would use their mighty legions to conquer an area, but once taken over they would leave a small force in place and install a governor to oversee and reorganize the providence. The Romans left most of the cultural institutions in place and also shared freely the benefits of loyalty; engineering, commerce and protection to name a few. With the exception of rulers and rebellious characters, most of the populous of a region was left alone provided they paid taxes and behaved themselves.
A similar approach was used in China, where leaders used brute force as well as benefits like trade, transportation and land reform to entice otherwise rebellious warlords to remain loyal to imperial leaders.
In North America, native leaders would to something similar. Creating strong bonds between tribes through seasonal trade of mutual protection alliances was common in the eastern woodlands, but in areas of the Great Plains they would put little emphasis on territory because of the migratory nature of their lives.