Answers have been accurate but let’s add some spice to make it easier to understand and more memorable.
The Federal Reserve has an accounting computer.
The core equation of accounting is: ASSETS - LIABILITIES = EQUITY. In other words, the value of what you own minus what you owe to other people equals your networth.
Now here’s where the magic happens. The Congress has declared that the liabilities of the Fed are the currency of the realm. Anybody can write a liability. I can write an IOU that says “I owe you one trillion dollars”. I’ve done this before. I wrote it and signed it and put it in my pocket to feel all special. But for real business operations, the trick is getting other people to accept your debt in exchange for other stuff that’s valuable. The Fed doesn’t have this problem because the Fed is part of the government.
When the Fed wants to issue money, they hand out IOUs. Because the Fed is a central bank, this is done through the banking system itself. The Fed can say to the banks “Hey banks, I want to buy one trillion dollars worth of assets from you.” And the banks will say, “Yeah okay, sounds cool.” So the Fed gobbles up the trillion dollars of assets and issues to the banks a trillion dollars of IOUs on its accounting computer.
ASSETS: 1 trillion
LIABILITIES: 1 trillion (computer)
Those liabilities are called United States dollars.
We’re ignoring all the other stuff that’s on the balance sheet at present just to focus on this transaction to make it simpler. Just this one transaction. And you can see, it’s just double-entry accounting. The Fed has purchased more assets which is must record, and simultaneously it has created more liabilities to give to banks in order to pay for those assets. Pretty simple. That is the first step of the process. This operation increased the monetary base of the US.
Right now that new money is still on the computer. Banks can have accounts at the Fed but private people like me and you do not. You’re asking about currency in circulation, and we are almost there. Those “liabilities” on the computer are basically the same stuff as green cash, as far as the Fed’s books are concerned. What this means is that those computer entries will be turned into green cash whenever the banks ask for it. It’s already green cash, it’s just being stored on computer instead of in a vault. So the banks just have to contact the relevant person and say hey, I’d rather have the actual physical green instead of the computer green. And the Fed is all like, no problemo. Other parts of the government are contacted in order to print up the cash, and that’s it.
ASSETS: 1 trillion
LIABILITIES: 0.5 trillion (computer), 0.5 trillion (printed cash)
The cash gets delivered in armored cars to the bank, where it’s placed in the local vault. And then customers of the banks like you and me make withdrawals when they want cash money. That’s how the physical cash leaves the banking system and enters the wider world. The 1.4 trillion dollars in circulation cited in the OP the stuff outside the banking system. It is still listed as a “liability” of the Federal Reserve on the books, but of course, it does not work like any other liability in existence.