This doesn't really apply to everyone in medieval times, but the Mongols had an amazing communication system called the "yam" or "Örtöö" that was basially checkpoints every 25 miles with riders who could deliver messages across the entire empire. Think of it like a Mongol Pony Express. Here is a cool passage from "Great Armies of Antiquity" talking about how they got riders to travel faster, like having them sleep in their saddles. This allowed orders to be carried all across the empire extremely rapidly (for a long time they also let merchants use the system free of charge until they started abusing it). Official messengers of the Khan carried his seal which meant that they message was legit and that messing with the rider meant extra punishment (messing with a regular rider pretty much meant automatic death but you seriously don't want to get in the way of a message from the Khan). The Mongols didn't usually use a supply train when they were going to battle because it would slow them down but I imagine (someone correct me if I'm wrong) that supply trains were typically they way that messages were brought back from the front lines during battle.

Sources: Trade, Travel, and Exploration in the Middle Ages: An Encyclopedia By John Block Friedman, Kristen Mossler Figg

The Mongol Conquests in World History By Timothy May