I haven’t seen anything specifically about this, so I figured I’d ask. It is also a difficult question for me to phrase, so I was unable to perform a simple search on the topic.
My question is specifically, how did people travel the world before the advent of the modern banking infrastructure? Did people just bring lots of money with them when they traveled? How did they deal with acquiring local currencies? Wouldn’t it be easy to forge a currency of a country that the recipient had never been to (for example, I’ll trade you these dollars for these yen, and I PROMISE that these are real dollars, even though you may have never seen dollars before)?
Certainly some people would arrive at a destination and take up a trade or a job, which carries with it it’s own set of challenges. However, there were rich people who would travel the world and I’m assuming they traveled mostly for leisure. For example, William Randolph Hearst traveled extensively with his mother when he was ten years old, in 1873. I assume that they didn’t work odd jobs while they traveled. Did they simply carry a trunk filled with money with them? Were there banks that they could withdraw funds from? Even this is comparatively recent. Certainly by this point you could wire funds across great distances, but what about earlier?
Banking has a long history, and had been around for centuries prior to your late 19th century example. The Knights Templar in the 13th century set up a system of promissory debit and credit notes that fulfilled the function of a transnational bank (Sean Martin, The Knights Templar: History & Myths, 2005.)
The question you pose of foreign exchange itself requires modern banking infrastructure to be in place. A central bank prints currency like yen or dollars, and by this point the nations concerned in the exchange were diplomatically linked and would hold foreign reserves. There would be no confusion as to what is legitimate currency if you were trying to change money legitimately, and not just attempting to buy things from small vendors with your foreign currency (which would likely not be accepted).
Even prior to central bank money, there was one common store of value that was valid all throughout the old world: GOLD. The value of coinage was measured not by the number of coins you had, but by their weight. 1 This provided a common standard of value even if you had travelled all the way from Spain to China. So yes, travellers would bring ample amounts of of gold with them, but keep in mind that barter and credit were the primary forms of exchange for most of history. (Yule, Henry; Cordier, Henri (1923), The Travels Of Marco Polo, Mineola: Dover Publications)
/r/urosSlokar12 answered some of this pretty well here.
The short answer is Letters of Credit. Paceminterris implies that a banking system was in place for this, but even merchants would do this at first: a Quaker merchant in Philadelphia, say, would have an arrangement with a Quaker merchant in London. You would give the merchant in Philadelphia $500, he would write a letter of credit for you, you would present that in London at the other merchant's, and collect. There would be a discount: some of that $500 would be retained as a fee, so you would not collect it all. And of course the London merchant could also write letters of credit to draw upon the Philadelphia merchant.
Eventually banks, like Barclay's , would do it, because the greatest problem for transfers would be those of merchants. If you send $5,000 for goods to be sent from London to you in New York, how do you know the merchant won't pocket the money? If he sends the goods, how does he know you'll send the money? The simple answer is to find a third party to hold the money. And for that kind of sizeable international transfer eventually there would be real sizeable institutions.
If you go back into the 18th c. and earlier, you'll find quite a lot of similar note-passing used in lieu of cash, not limited at all to international transactions. Do a job for George Washington, and he might give you a note for it. You might then pay for something yourself with George's note. A bank might issue some fixed value notes- fancier, harder to forge- called banknotes.