Rome, Venice, France, etc. Were all rich in the Middle Ages, but where did they store the money? Rome paid it's soldiers with a salary, but where would this money be kept at and how would then actually deliver it to the soldiers?
Rome had a temple devoted to its monetary policy, the temple of Juno Moneta. Andy Meadows has a nice article about it in JRS. It's on JStor if you have access; it was the first hit for me googling "andy meadows Juno Moneta." It was the mint. The treasury was in the temple of Saturn.
The process of minting coins is pretty straight forward. You cast a flan (a blank coin) and then strike it between two carved dies to imprint the image. This is an easy thing to do and mints operating in this fashion could produce tens of thousands of coins in a few days. It's also easily movable. Many generals minted coins in the field, so there wasn't need to ship coins from Rome to the soldiers as long as the general had access to a mint.
Howgego's book is a good introduction to numismatics if you're serious about getting into the topic.