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.