In Ancient China, the primary method of coordinating units were to use flags, drums and gongs. Beating drums was a signal to advance, whereas ringing gongs was an order to retreat. The use of flags instructed units on the battlefield to move in specific directions.
(Wuzi, chapter "Reaction") The method of war is always to command with flags during day, and with gongs and drums at night. Move left when the flag points left, and right when the flag points right. Advance at the sound of drums, and stop at the sound of gongs.
Such commands could be issued and carried out because these armies were not masses of random strangers thrown together. In fact, Chinese armies possessed a full hierarchy of units during the Warring States period. Generally speaking, an army had a fighting strength of 12,500, evenly divided into five divisions of 2,500 each. Each division in turn consisted of five 500-strong brigades. Below the brigade level, there were smaller units of 100, 50, 25 and 5 men.
In a battle, therefore, more specific orders or intel could passed down through the ranks via the chain of command, usually by dedicated messengers. This complements the use of flags, drums and gongs for broad coordination to realise effective command in a battle.
Logistics were primarily reliant on having stockpiles of supplies. Ancient Chinese states were agrarian societies, and governments taxed their peasants in kind. Surplus rice would thus be stockpiled for military use. Consequently, these states generally did their best to improve agricultural productivity, and reforms were major factors in improving a state's military performance.
When war breaks out, although an army would march into the field with whatever supplies it could carry, this would have been only good for a few days.
(Hsuntzu, chapter "On War") The elite soldiers of Wei wear three layers; wield crossbows of 12 stones with 50 arrows; are equipped with halberds and swords; and they can carry three days supply of food.
Thus, the primary means of keeping an army fed were supply trains. Every war involved numerous wagons responsible for replenishing an army in the field with supplies from the state's central stockpiles.
(The Art of War, chapter "Waging War") Wars are fought with a thousand chariots, a thousand supply wagons, a hundred thousand soldiers, and food is delivered across a thousand miles.
Occasionally armies would harvest the farmlands of their enemies as well as forage, but for the larger armies of the late Warring States era, supply wagons were a necessity.
There were no armies of several hundred thousand strong during the Three Kingdoms period. However, the largest engagement of the era, the Battle of Red Cliff, did involve over 200,000 troops under Tsao Tsao. In that example, his forces were divided into two main prongs as well as six smaller groups, which were either held in reserve or advancing towards other targets. Within each army, individual general commanded smaller units of perhaps 5,000 soldiers each.
Therefore, not all 200,000+ soldiers were physically present at Wulin, where the famous burning of the ships took place. Note that some have argued that Tsao Tsao's forces totaled ~220,000 overall, i.e. some were left in the north to guard his homeland. In this interpretation, perhaps no more than 100,000 actually took part in the battle.