How did currency exchange work in the Middle Ages, especially if the coins are not recognized?
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In principle, a coin is worth its value in precious metal, plus or minus what the locals think of the issuing authority. So an unknown silver coin weighing half an ounce would be worth 'half an ounce of silver in local coinage' less the expected costs of melting it down and re-coining. The Vikings, who didn't use coins as such, used 'hacksilver' as an intermediate stage between barter and coinage: if you agreed to pay an ounce of silver but only had a four-ounce candlestick, you cut a quarter off it with a hacksaw.
This is obviously unsatisfactory for any form of long-distance trade, so there were professionals called money changers, who would inspect a foreign coin and buy it for its value in local currency, less a percentage to cover the moneychanger's expenses. ("Money changers would assess a foreign coin for its type, wear and tear, and validity, [and purity, presumably] then accept it as deposit, recording its value in local currency", Wikipedia). Obviously, if the moneychanger could then sell the coins to somebody travelling in the right direction, a double profit could be made. Often, the moneychangers were Jews, who were often barred from owning land, had a high literacy rate and maintained contacts with co-religionists in other areas; the network could be regarded as a rudimentary banking system.
OF course, in the fifteenth century there arose proper banks, who would issue letters of credit when you paid into your local office, redeemable at your destination in local currency. (The Knights Templar did something similar for pilgrims around the time of the Crusades; but after they were suppressed for idolatry (oddly enough, by one of their debtors) the idea fell out of favour for a few centuries).
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