In a textbook I was once asked to review, the author was discussing the ancient Romans (but it might as well have been medieval people): "They did not drink coffee or tea. They did not drink distilled spirits." The distinct impression the book gave was that ancient Romans were a bunch of Mormons.
Now of course, as I noted in an earlier post, a lot of what we eat but medieval people did not is food from the New World: corn, tomatoes, chocolate, potatoes. But tea and coffee are not New World products. They still didn't drink them in medieval Europe--any more than distilled spirits (which as the name suggests, requires distilling, not invented yet). This is because they did not have them.
(Yes, I know, in my stories people drink tea. This is because, in spite of the medieval-looking setting, my stories are actually set in an alternate version of the nineteenth century, a version where the Middle Ages never ended. I've explained this.)
Tea originated in China, leaves from a local shrub brewed in hot water. It was drunk there from at least the first century AD on. There are various legends about generals ordering their men to drink tea instead of straight water, which required boiling the water, thus killing off germs that were meanwhile incapacitating the other generals' armies. Although this appears like a tall tale, the bitter infused leaves do seem to have begun as a medicinal drink. The western word 'tea' is derived from the Chinese word.
From China tea spread to other parts of Asia, especially Japan and Korea. But it did not first reach Europe until the sixteenth century, when Portuguese explorers brought some back. In the seventeenth century the Dutch East India Company started importing tea, which became popular as a luxury drink in Europe. Not until the nineteenth century, when the British began having India (then part of its Empire) start growing tea in order to break the Chinese monopoly, did tea become the all-purpose British drink it still is today. (Tea has also become very popular in India in the last 200 years.)
Only in the West did tea get drunk with milk and/or sugar; in East Asia it was (and is) taken straight. Iced tea, which is the predominant American form of tea, is essentially unknown in the rest of the world.
Coffee was also unknown in medieval Europe. It is brewed from roasted and ground coffee "beans," which are actually the seeds of a berry native to Africa. It is first known to have been drunk in Arabic regions, probably around the fifteenth century. From there it spread to the Ottoman Empire (roughly what is now Turkey) and, by the seventeenth century, had become very popular in Europe. Coffee houses sprang up, where people imbibed this exciting and stimulating beverage.
Louis XIV is reputed to have received a coffee bush from the Ottomans, one that produced especially good coffee beans. This bush is the ancestor of all "arabica" coffee cultivated today. Modern Latin America is where most of the world's best coffee is now grown, but it really only began to be planted there in the eighteenth century. North Americans started to take up coffee drinking in preference to tea during the American Revolution, when the British heavily taxed tea.
We now take our morning hit of caffeine for granted. Medieval people would have rolled out of bed and either had nothing to drink or else a satisfying mug of beer. It would certainly make one's mornings take on a different complexion.