Until European rulers discovered fiat currency by adulterating the coinage, coins simply had the value of however much they weighed. There was no need for exchange rates, because you just weighed the coins and that was what they were worth. Standard-sized coins gave convenient ranges of values which reduced the need for weighing, but ultimately the weight was the value.
This meant that although every country around Europe had its own sizes of coins, there was no real "monetary system" as we would understand it today with fiat currency and exchange rates. The "monetary system" was simply that a certain weight of gold or silver was worth a certain weight of gold or silver, and that was all there was to it.
In the absence of a major centralising authority in Middle Earth, it seems likely that this would be the same there too. This is purely hypothetical though, and Tolkien hasn't given us strong evidence of any of this, beyond the fact (per Smaug's hoard in The Hobbit) that coins do exist.