Okay, to start, the Middle Ages was not the Dark Ages. The term "Dark Ages" was coined by British scholars to describe the period, basically the sixth century, between when Angles and Saxons arrived in Britain (c. 500) and pretty much obliterated the Christian, Roman culture that was there in England (including the historical King Arthur), and when Christian missionaries reconnected England to the European mainstream (c. 600).
Now of course England is not the world (though to listen to some Brits, you might think so). (Gee, they're almost as bad as Americans!) But the sixth century was tough in a lot of places. The Roman Empire (then centered in Byzantium, capital Constantinople) had shrunk, and the areas that are now France and Spain had "barbarian kingdoms" (respectively Franks and Visigoths) that were only very nominally in the Empire. Then there were such disasters as global cooling and the Black Death.
And yet trade continued through this "dark" period, with sixth-century Byzantine coins, pottery, silver dishes, glass beads, even fabric found all over the Old World, especially Eurasia, as indicated by dots on this map.
This map was worked out by the British archaeologist Dr. Caitlin Green, on whose blog it was originally posted. She gives a lot more detail, which I recommend. Here note that while the Byzantine Empire in the sixth century (solid brown on the map) was fairly restricted to the Mediterranean (and not even all of that), including what's now Italy, Greece, Turkey (then Byzantium), the Near East, and bits of north Africa, Byzantine artifacts from the period have been found in Africa, in Asia (including India, China, and Japan), and in western and northern Europe, including Anglo-Saxon controlled Britain.
Now Byzantines themselves didn't go to all these places, but trade routes did. Ships sailed down the Red Sea, and either continued down the African coast or went around the Arabian peninsula and on to India, where many artifacts have been found. There were trade routes carrying Byzantine goods across the Sahara. The silk roads across central Asia to China carried great luxuries to the Mediterranean. A Japanese monastery still has a silk cushion cover (pictured below), given to it by the Japanese emperor in the eighth century, which was created in sixth-century Syria, from silk imported from China, and which then followed the silk roads back.
Byzantine gold coins have been found in Scandinavia, where the local people had long traded fur and walrus tusks—used as ivory—to the Romans and continued to do so. Indeed, Scandinavian settlement of Greenland was, centuries later, driven by catching walruses for the ivory trade. Although the Scandinavians themselves did not have a coin-based economy in the sixth century, they certainly recognized their value. This gold coin minted in the early sixth century for Emperor Anastasius was found in Sweden and was pierced for use as a pendant.
Much of what archaeologists have found comes from burial sites—in England the bodies buried with them sometimes have DNA suggesting a North African origin. Others were hoards that were buried when the person who buried them must have intended to hide them until able to come back, but then never came back. Some, like beads and pieces of pottery, were lost accidentally or were tossed out when broken and no longer wanted.
The vast spread of Byzantine goods along trade routes, routes that continued even in a politically, socially, and economically deeply troubled time, indicates that there has never been a time when people could shut themselves up behind high walls and pretend the rest of the world didn't exist. (On this see more here.)