By aide-de-camp or other messenger. My answer will mostly reference examples from the very late 18th century and early 19th century, but systems did not change overmuch from the height of 18th-century warfare to the Crimean War in the mid-19th century.

In the middle of battle, a general would usually issue an order in both in writing and verbally - some generals wrote them out personally, others, like Napoleon, who famously had near-illegible handwriting, dictated them to a chief of staff - which would be given to an aide-de-camp (a trusted officer, often but not always young and hungry for advancement) whose job it was to make his way to the subordinate commander in question and deliver the order. If time was of the essence, an order might be given only verbally, but this ran the risk of the aide garbling the instruction. A written order gave the subordinate commander absolutely precise instruction, but took longer to write and read, so might mean the crucial moment was lost.

Commanders would usually brief their important subordinates with the general battle plan or issue general orders the night before a battle, so those subordinates knew what the plan was and their objectives were, and could thus act on-the-spot to achieve those objectives (making this process simpler was one of the main impetuses behind the development of the divisional system, and its later evolution into the corps d'armée). Thus a general would not, hopefully, need to micromanage each of their subordinates.

Generals would also usually position themselves with a reserve or at a crucial point in their line so they could oversee matters themselves. Napoleon famously kept his reserve near him so he could issue the order to advance at the precise time his enemy was weakest. If he got a report that things were in a particularly critical condition, a general might move to the threatened sector and take personal charge.

Other techniques did exist, but they were often not very reliable and overly simple. Optical telegraphs were developed during the French Revolution, but they were too bulky to be used in battle, and in any case powder-smoke would make optical signals difficult to see. Particular patterns of artillery fire were considered as a way to signal distant units to begin an advance, but these were often difficult to hear over the roar of battle. Simple smoke and light signals were possible, but these had the disadvantage of letting your enemy know that something was about to happen, and, again, were very simple and prone to failure. The most reliable method of communication was still a man on a horse.

Sources:

Swords Around a Throne: Napoleon's Grande Armée by John R. Elting

The Campaigns of Napoleon by David Chandler

Redcoat: The British Soldier in the Age of Horse and Musket by Richard Holmes