As I played medieval 2 total war, I noticed all money was counted in "florins". Seeing that not every country had the resources to produce their own currency, would merchants traveling across countries use the same coinage to avoid confusion? And if not, who decided the exchange rate of the money?
All currencies (aside very few brief and isolated examples) in pre-17th century Europe would have been commodity currencies of gold, silver or bronze rather than Fiat currencies (i.e. currencies as we understand them today).
How coinage works in a commodity currency market is actually very straightforward - a city's mint would set the standards on how much (weight-wise) of a specific precious metal at a certain minimum level of purity constitutes a single unit of currency (e.g. a Florentine Florin would be a coin consisting of approx. 3,5 grams of gold). Principially any person could take that amount of precious metal in to the mint, pay the mint's fee and have that gold shaped into a florin piece - the stamp and seal on the coin have no other meaning than "The x Mint has checked the quality and weight of this piece of metal and certifies it to be y grams of said metal."
Therefore the only cost of establishing a commodity currency would be the actual running costs of the mint (which would often pay themselves through issuing fees). In fact quite a few of medieval currencies were actually established by merchants themselves rather than state governments.
Merchants travelling between countries would tend to use the currencies with the widest recognition, as it would significantly ease their lives - for most of middle ages the Florentine coinage (esp. the florin) was the gold standard (pun intended) of currency with regards to trans-country trade - Florentine banks and businesses were already large and influencial enterprises and trading in a currency they accepted was convenient for most. However even if there was a merchant that did not accept a specific variety of coinage, the issue was easily rectified - as the coin is made of the actual precious metal, it could easily be restruck into the local currency at the local mint.
Accordinly there were no exchange rates as such either - everything was based at around the value of the actual precious metals in question - one Florin would be exactly the same 3,5 grams of gold in Florence, Venice, Paris or Vienna and would essentially be worth the same, in the local currency it might just be struck into coins in slightly different denominations.
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