In the series Game of Thrones, the character Varys is shown as having spies all across the country feeding him information. How common was this in medieval Europe? How would one aquire a vast network of spies?

From payment records in the (very) late Middle Ages, when we have them, it seems that a lot of the hiring of spies occurred on an ad hoc basis. When cities and nobles in the Low Countries went to war amongst themselves in the 15th and 16th centuries, for example, it was not uncommon to hire one person or a small group to stake out a particular location for a few days and watch for enemy soldier moving through there. In 1511, for example, a small posse of spies from Haarlem avoided detection on the roads by taking a sled across frozen Lake Haarlem to a watch point on the border with Utrecht. This was a one-time payment. During the Hundred Years' War, too, the English government would hire fishermen to watch for French sea movement.

However, city records also reflect the existence of so-called "secret friends"--longer-term relationships with a lookout, or perhaps a bureaucrat in another city. That is, they reflect payments to these "secret friends." Unfortunately, we don't hear much about how they started spying or what happened to them afterwards--only the occasional tantalizing hint like the payment rendered to the widow of Hendrik Faes (also in 1511).

As far as more widespread networks go, though, the two most flexible and popular ways to obtain information were through ambassadors and messengers. Ambassadors made great spies first of all because of their freedom to travel, and second because by the very nature of their position they had access to people of at least some power. It's important to remember that in the days before news in the modern sense (a MASSIVE rumor mill, to be sure, but not journalism like today), "espionage" could mean gathering information simply about what had happened. The example I love is the English accusing Scotland of spying simply for knowing that the 1381 Peasants' Revolt had happened. (...)

Messengers also had freedom to travel without suspicion and were a readily organized group. One aspect of their utility came in their carrying of letters. They could convey the information written down, but also, they were the ones who knew the oral component of messages--medieval letters were often mostly placeholders for the real message. But also, due to the freedom of movement, they might be instructed to peek into dark corners and bring back observations of what they saw. In general, wartime courier-spies were those who had the job during peacetime; they were approached and paid more when fighting threatened.

It wasn't unusual in medieval Europe for people to carry out long-distance, long-term friendships entirely by letter and messenger--never actually meeting in person. It stands to reason that long-distance spies would be recruited the same way--have a trusted messenger (ambassador, courier, merchant) and make sure they had ample money to buy some new loyalty.

Oh, yes--a not uncommon note in sources is recompense for a courier-spy who had been robbed along the way.

ETA: I offer some sources on espionage in the medieval world in this earlier thread.