How would new money go into circulation lacking a central bank issuing the currency?
Back in the days of National Bank Notes, and before the Federal Reserve, a bank would do much the same thing except with the Comptroller of the Currency.
Before the National Banks and their notes, banks were free to print as much paper money as they wished. Of course, if they printed more than they could cover with hard money when presented for redemption, they'd get into trouble, and often did, whether because of fraud or a bank run.
Speaking of hard money, back in the days of free coinage you'd bring some gold or silver to a mint and pay a fee to have it minted into legal tender coinage. (The free in free coinage meant you were free to have as much of it turned into coins as you wished.) Free coinage of silver halted in the United States in 1873 when we went on the gold standard and abandoned the absurdity of bimetallism.