During that time, money would have been in gold and silver coins, not in banknotes. Gold and silver has a value of its own, called the melt value. All that coins did was standardize the weight and the alloy, so you could be fairly certain how much gold/silver you get without needing scales.

So while foreign coins might have been more problematic than local ones, they would still have been accepted by those who were familiar with them and were certain what kind of alloy they are.

They might need to weighed to see how much gold or silver is in them.

/u/satuon gets us half of the way there. The other half is that coins were often minted to somewhat universal standards. For example, in Europe, the florin became the de-facto currency of account. The florin was the first wide-spread minting of a gold coin in the medieval period, which was theoretically very similar in value to the Byzantine hyperpyron to which it was a contemporary. These florins, both in design and nominal 'weight' were copied in major trading centres across Europe, from Hungary to Amsterdam. Areas that were less trade rich still relied mostly on the previous method of account, the mark, which referred to a weight of precious metals rather (similar to the use of the talent as a unit of both weight and account in the ancient world). So, you might have a transaction that could be in florins or in marks, and when being paid those florins or marks would, theoretically, be of a similar weight of gold.

That said, gold coins were not going to be coins of every-day transactions. So, coming back to your original question, how would people take money from one place to another? The answer is actually pretty much the same: the florin. Or rather, what the florin represents, which is the early medieval banking system and it's spread. You could take promissory note from one bank branch to another, along with supporting documentation of course. Those banks would keep those accounts in florins, and be able to convert to local currency on demand based on local rates of exchange.

What they said, really. Here's a transcript of the total income of the Danish Crown in the fiscal year of 1563-64, and you'll notice coin and metals were from all over Europe. The reason its origin is important in the accounts is that the actual content of precious metal would vary.

"Mønt" means coin and refers to Mark, while the "Daler" (German: Thaler; English: Dollar) is the North European silver version of the Florin, u/Spoonfeedme mentioned.

"Klippinge" means part of the coins had been cut off for re-minting, but rulers would try to make people accept these now less valuable coins as the real deal. It never worked for long, though, which is why you cared about the origin of the coins.

So, to add to the answer to your question, if you had occasion to receive money in different currencies, you'd know the current values of a lot of different coin, but also try to keep tabs on what coin had been re-minted at a lower value recently. It was a bit of a game, but if that was your business, it probably wouldn't seem as difficult, as it does to us now.

Sources: Grundtvig, Johan: Frederik den Andens Statshusholdning (1876) (image from here)

Balle, Søren: Mønt, vægt og kornmål i Danmark i 1500-tallet (1987)