Was it important to keep the exchange rate updated as often as possible? How did banks know what rate to apply between countries across the Atlantic before the telegraph was laid? Was the possible discrepancy between coasts a problem, until a ship would arrive with the mail?
Before 1914, most if not all currencies were pegged to gold or silver and often minted in those metals.
Let's have some examples (this is for the time immediately after the Napoleonic war).
A pound sterling was 20 shilling coins, each containing 5,56 grams of 92,5% silver. A guinea, an older gold coin contained 8,5 grams of 90,9% gold and was officially valued at 21 shillings, while the newer sovereign contained 7,98 grams of 91,7% gold and was valied at 1 pound sterling (20 shilling).
Likewise, the Spanish dollar (their version of the German thaler), an 8 real coin (thus the famous pieces of eight from pirate lore) contained 27.47 grams of 93,1% silver) and the gold dubloon, a 32 real coin, contained 6,77 grams of 91,7% gold.
The Austrian thaler contained 28,07 grams of 83,3% silver and the Austrian gold ducat contained 3,55 grams of 99,5% gold. Interestingly, the Austrian thaler became the de facto currency of much of the Arab world and Ethiopia.
The French silver Écu, a 5 franc coin contained 25 grams of 90% silver while a French gold Napoleon, a 20 francs coin contained 6,45 grams of 90% gold
Swedish riksdaler silver coin contained 29,25 grams of 87,8% silver while foreign gold coins were used (primarily dukats) until the Scandinavian monetary union, where a gold coin valued at 5 kronor contained 2,24 grams of 89,7% gold.
The mixed gold and silver standard caused some problems - the price of silver fluctuated a lot more than the price of gold, especially as the production of the Spanish silver mines in South America brought large amounts of silver to Europe and the trade with China later drained silver, as the Europeans paid for china, tea and silk with silver coins, as the Chinese were not interested in anything the Europeans produced (which caused the British to start growing opium in India to sell to the Chinese, which caused the opium wars, but that is a different story).
At times the value of gold was higher than the nominal value of the gold coin, and many British guineas were melted down and sold for their gold value as their gold content was worth more than 20 (earlier value) or 21 (new value) shillings in silver, causing gold to dissapear from circulation and causing problems when doing business with larger values. Later the opposite became true, as 28 000 tons of silver was shipped to China in exchange for their goods, and silver became scarce, making nations go on a double or gold standard, issuing notes for larger value silver currency.
Several attempts were made during this era to standardise coinage to help trade across borders. The Latin Monetary Union saw France, Spain, Belgium, Luxembourg, Greece, The Papal States, Italy, Switzerland, Greece, Bulgaria, Romania, Russia, Finland, Tunisia and Serbia all agree to mint coins with the same weight in gold and in silver so that any coin minted in any nation could be freely used in any other nation. However, both The Papal States and Greece eventually debased their currency. The union also faced stress from the changin value of silver, which went down compared to gold when new mines opened and new techniques for mining silver came to light in the second half of the 19th century. The Latin monetary union pegged silver to gold at a rate of 15,5:1. German merchants would travel to France and Belgium, have their silver minted to coin, exchange it to gold coins at 15,5:1 and return with gold and a tidy profit. France was forced to disallow the free minting of silver in the Latin monetary union in 1874 and the whole monetary union were effectively on a gold standard from 1878 onwards. However, both France and Italy printed bank notes to a larger extent than they could convert to gold, and when most nations went off the gold standard 1914, the union ended, even if it existed on paper until 1927 and the Austrian mint still produces coins according the standards set by the union for collectors.
Likewise, the Scandinavian monetary union made Swedish, Norwegian and Danish coins interchangable between each other.
That said since before 1914 coins, regardless of who minted them, were minted out of gold and silver, and the weight of the metal in the coins were known. Unless the coin was counterfeit or shaved (a process were people would shave thin shards of the coin's sides and still use it to its full value, and the basis of rifled coin sides) you knew its value compared to your own currency and could accept them as payment.