Since the fire missions were direct fire, the Battery Commander made most of the firing decisions. He would have been given orders about the location of his battery, what he was supposed to accomplish, and when. Once the combat started he would make decisions based on what the enemy was doing.
Both then and now the idea is to concentrate fire on a particular target. Back then you had to be able to see your target, today it is more likely indirect fire. Hope this helps.
The following was taken from "Robinson Battery, 1st Michigan Lt. Artillery"
CAPTAIN (Battery Commander)
Had overall command, control, and responsibility for the training, serviceability, and combat operation of the battery's personnel and equipment. He was not only the chief recruiter of the company, but also used his influence to acquire horses and other material, through means outside normal requisitions, to keep his battery in the best possible condition. Depending on the organization of the army at a particular time, the captain received his orders from either an artillery battalion commander, a division "Chief of Artillery", or an infantry brigade commander; ranking from major to brigadier general respectively. The captain had command over as many as 170 men and 98 horses in a six gun battery with six horse teams. In a four gun battery with four horse teams he had to have a minimum of 71 men and 45 horses to function efficiently. Most artillery officers were very slow to receive promotion due to the relatively light casualties and "turnover" in the long arm as compared to the infantry.