The Fed doesn't print currency - thats Treasury, although the Fed holds and distributes it to depository institutions! They control the money supply by reducing the fractional reserve lending rate at banks (reducing supply of loans), increasing interest rates (reducing demand for loans) and unwinding their balance sheet by selling back purchased assets (largely t-bills, reducing circulating supply directly).

The money supply of centrally banked economies is mostly debt/demand driver, not supply driven. Money is created when lent, and destroyed when repaid. By tweaking parameters, the Fed is able to manage circulating supply.

It's actually a really elegant system, IMO.

Paradoxically, the default state of fiat currency is deflation, because the primary means of money creation is debt. If inflation is 2% every year that means future debts must overshadow past debts. If you raise interest rates people stop borrowing money because it becomes too expensive. The interest rate itself acts as a productivity gate. "You must be this productive to obtain financing." If you stop borrowing money, then the only place for the money to go is to pay off debts, which contracts the money supply and you get deflation which is strong enough to counteract past inflation. The vast majority of dollars were "printed" this way.