We take transportation for granted. Need to pick up a few things at the store? Jump in the car. Want to get to Europe? Get on a plane, and you'll be there in the morning. Even in the nineteenth century, when you got on a train you could be as far away from where you started in an hour as you would be after a long day on a horse.
Transportation in the Middle Ages, however, required animal power, not machines. For most people, the way they got from one place to another place was by walking. Armies always had large foot soldier contingents, which meant they traveled no faster than someone could walk carrying a pack. For the Hundred Years War, where we know in some detail about military movements, soldiers would hike 20 miles in a day plus fight a battle. They were tough.
Once stirrups and saddles and horseshoes were developed, the well to do would ride. You could cover a lot more distance on a horse than on foot in the same amount of time, so riders would also need pack horses to make sure their supplies arrived at the same time they did. Riding is of course much more tiring than sitting in a car, so the aristocrats who rode across Europe (as they did) would also have had to be tough.
Draft horses, that is horses that would draw carts or plows, really only came in at the end of the Middle Ages and were too expensive for most. So carts and wagons were pulled in most cases by the faithful ox. A donkey or mule might also sometimes be used (the donkey if the wagon were light). The faithful ox was very strong but also slow; in the nineteenth-century US, when covered wagons were usually pulled by oxen, the wagons would be happy to make 10 miles a day.
The wagons, used in the Middle Ages to take produce to market and the like, did not have the springs or brakes of modern wagons. You probably would not want to ride in one for more than short distances. Buggies and carriages, then unknown, would have seemed very luxurious to a medieval peasant. On the other hand, unlike modern drivers who, with few exceptions, have no clue how their car actually works ("You turn the key and push these pedals!"), medieval peasants knew all about their wagons.
As all of this suggests, going more than five or ten miles from home was a major enterprise. It is thus somewhat surprising how often and far some people traveled. Even if one had a good horse, a big challenge was the roads. Most roads were dirt, which meant very uneven and potentially very muddy. There was nothing like a modern road map or modern road signs, much less GPS. Routes did not have numbers. You had to know where you were going. There were handbooks that told one landmarks to watch for, but there was also heavy reliance on stopping and asking people.
The best medieval roads were the Roman roads, still in use, cutting straight across the landscape, paved in stone that might have heaved and buckled some over the centuries but was still a lot better than muddy tracks. Some of these Roman roads even had occasional road signs, This way to Alesia. These roads did not always go where medieval people wanted to go, however, because the population centers had shifted since late antiquity, and some previously important Roman towns were now tiny hamlets, if that.
One of the challenges for any road was getting across a river. Building bridges, as I have previously discussed, was an important economic activity for medieval towns, to make sure people and goods could reach them easily. A surprising number of these old bridges are still in use.
The easiest way to transport heavy goods was by water. Wine, for example, would be floated downstream, the barrels loaded on a barge. Water transportation was slow, but it required far less energy, because the river provided much of the momentum, and a boat will hold a much heavier load than you could put in a cart that you were going to try to drag down a muddy road.