So, this is a summary text of historical changes, and then you can research better for it on technical sources. The intention is to have a base of assimilating infos to compare. Also, feel free to give any feedback. We will see the international monetary system, that's also an intro to macro indicators, to understand how the trade balance works.
Before paper money was invented in Asia, the coin value itself was determined by the ammount of minerals it had (weight), so trades were already made in that time, through especulation on changes of coinage, besides de mercantil usability itself. The variation of one to another basically depended on that, keep in mind there were a lot more variety of currencies due to division of regions by feuds at some times, so political and military factors also might have influenced in its liquidity... Before that it was a barter like trade economy.
We see an increasing supply of money through all history, since the creation of banks and interests rates, part of total supply was already physically inexistent (imagine how fast this invention compounds through the ages on total supply, its insane to even think), and paper money was a great resource for that. Till nowdays it's obvious that very few of it can be converted, also why "bank runs" makes no sense, it would only takes the liquidity from the market, and risk the economy... Besides money being turning into digital with the internet... And this constant rise is the explanation why there were few millionaires times ago, then few billionaires nowdays, and in the future some few trillionaires and many more billionaires, also due to higher gdp per capta, but inconstant real gdp or real wage (discounted inflation).
(Couldn't find any other more accurate image, the extended version also compares with stock market, real state and derivatives, you can see the ponderation of physical money in the top right).
Continuing, the first international agreement was the gold standard, where printing of money was pegged to gold reserves of the economy, a coverage as collateral. By changing its gold reserves on countries trade balances it would be changing the currency value in parity with others.
Whats the trade balance itself?
It's the net result of all operations between countries, it's own goverments, institutions and population. That includes importations and exportations of commodities, industrialized and comercials goods, services, properties, also financial deals, domestic assets, stocks, forex, derivatives, etc... So, this will impact in the currency exchange rate due to surplus or deficits on it. The country can try to control it by changing the cambio tax on importations or exportations. Also, inflation can be some of the determinants on those trades exchanges... Thats a subjective interpretation: If some currency worth less, it's more convinient that people takes money out of this fiat (to not lose international buying power), of course there are others factors involved, like the increased demand for exportations on commodities of a currency that is cheaper.
This is a chart from Brazil.
What happened was that due to comercialization, wars and international deals, United States and France detained mostly of the world reserves. Some countries already stopped the gold standard like England, and many others small countries prefered to hold US dollars as a strong currency backed by gold.
The next deal was the Bretton Woods agreement in 1944, that was an accepted propose at time of turning all currencies pegged with the dollar, that would have this coverage with a fixed value, so those fiats currencies could fluctuate some few percentages in parity with dollar. However it didn't work due to variety in correlation on US dollar/gold, some changes on this parity due to inflation... Also, sometimes US just had deficits on trade balance due to its own needs of imports and military spendings in other countries expeditions.
There was another similar try, called the smithsonian agreement in 1971, to peg all currencies with the dollar, but it also didn't work due to market fluctuations, dollar started to get devalued, countries decided to leave and let their fiats floating, and thats why we say that we have a floating exchange currency rate, also the public debt is floating. No, it doesn't mean it's neoliberal.
Also, all those measures didnt restricted FED's policies, that by curiosity was created after the crisis of 1907 with the help of international economic committees.
[Want an anime about economics? Try "Spice and Wolf", kind monotonous middle age view, but top rated stuff, and lets wait the "World End Economica" gets released after the game.]