The way that medieval coinage would generally work is that a decision would be made about how many coins would be struck from a given weight of metal, which would therefore indicate the value of the individual coin.
So to take the pound as an example, starting with King Offa of Mercia, the Anglo-Saxons established that 240 silver pennies would be struck from one pound weight of silver, and further than one penny was worth four farthings and twelve pennies were worth 1 shilling (which meant that twenty shillings were worth one pound). Offa in turn was borrowing from Charlemagne, who established that one pound of silver was equal to one livre, which was worth 20 sous/sols, which in turn were worth twelve deniers. Keen eyed observers will note that the notations for the different currencies – l, d, s – are the same in the British and Frankish systems. The reason for that is that Charlesmagne and his copiers in England, Italy, Spain, etc. were in turn copying Roman currencies: the “l” stands for “libra,” the “d” for “denarius,” and the “s” for “solidus.”
In other words, tradition and culture matters. Rome was associated with a commercial, currency-based economy and even after the fall of the Roman Empire, the memory of that economy was still strong, so associating your coins with theirs went part of the way towards ensuring that people thought your currency was good.
So for gold coins, you’d figure out how many coins would be struck from how much gold. Again, to take the English example, the “noble” was the first English gold coin to circulate widely. Originally, the noble was 138.5 grains or 9 grams of gold, so that one pound of gold would produce 453 or so nobles.
However, one thing to keep in mind is that, with a metallic standard, the government has to be careful that the cost of the coin doesn’t exceed its value (which means you’re actually losing money by making it), and there’s always an incentive to exercise the right of seignorage by declaring the face value of the coin to be greater than the actual metallic content of the coin (which means you’re making money by making money). Combined with the constant problem of private individuals producing counterfeit coins by clipping, sweating, or plating, the actual weight and purity of the currency in circulation tends to change over time.
OP, a good way of thinking about it for worldbuilding purposes:
The coin is worth nothing. It’s the quantity of metal that is worth something. The coin is merely a convenient form for the metal to take.
You know how scales are associated with merchants and trade? They have that association because any good merchant or tradesman would have a set of scales with weights (and the laws regarding this could get complex and intricate real fast) and they’d stick your coins on the scale when you went to make a purchase. If you gave them coins that were supposed to equate to a certain weight of metal, and they come in below that weight because they’d be sweated or clipped, they’d be all “you still owe. Put coins on the scale until it balances.”
That request could actually lead to MORE clipping; in order to make the scales balance, you might need more weight than was in X amount of coins but less weight than was in X + 1 amount of coins. So you’d take a coin and clip off a piece. (This might or might be illegal depending on the jurisdiction or the coin issuer; some coins were DESIGNED to clip.)
And of course this could all lead into more areas of fraud and abuse, because the scales have trouble detecting coins that have been adulterated, and unscrupulous merchants might doctor their weights, so as to slowly collect extra 1/50th of a pound weights of metal over a long period of time…
This is largely accurate, but as someone who’s read his share of MMT, there is one important proviso: the coin matters a lot when it comes to taxes and government purchasing. So even if the coin is debased, if that’s the unit that taxes are paid in and which you get paid in when the king’s soldiers show up looking to buy grain, it has value from that.
Which brings us to the non-metallic currencies that existed in medieval societies. See, in a world in which there’s a lot of barter rather than currency-based commerce because precious metals are scarce and a lot of people are subsistence farmers, tally-sticks would be used as records of tax payments or public debt. And because their value was back-stopped by the ability to turn them in lieu of tax payments or as letters of credit, they circulated as currency.