How do they “increase the monetary base” then? They don’t actually print more money.
Although the Monetary Base does, indeed, include currency (printed money in the form of dollar bills), printing more dollars doesn’t increase the Monetary Base. That’s because the Fed doesn’t just give that new money to the banks; they trade it for excess reserve balances. So printing doesn’t increase the base because the new currency is offset by the reduced reserve balances (which are also part of the Monetary Base.) The Base stays unchanged.
The Fed increases the Monetary Base by purchasing securities from the banking system and/or its customers. When they purchase a billion dollars of securities, they issue a billion dollar credit to the bank’s asset position in the form of a new reserve balance on the books of the bank. That directly increases the size of the Monetary Base (which is composed of currency in circulation plus bank reserves) by the billion dollars involved in the transaction.
If a customer sold the bonds instead, the bank still ends up with the billion in new reserves, but instead of those reserves replacing another bank asset, the bonds they held in the above example, they are offset by a liability of a billion dollars in the form of a customer deposit. (The customer delivers the bonds to the bank in return for a billion dollar credit to his account. The bank then delivers the bonds to the Fed in return for a billion dollar credit to its reserves.)
That process used to get money flowing in the economy because banks wouldn’t just sit on unused (excess) reserves. However, now the Fed in all its wisdom first puts trillions of excess reserves into the system and then pays the banks to sit on them. If that sounds silly, it’s because it is. Essentially, the QE’s resulted in the Fed forfeiting the control it once had over the money supply. Now they just control bank reserves and the money supply goes in whatever direction it chooses, depending upon economic activity, interest rates, etc.