It is worse and vastly more complicated than simple monetization of debt (US buying US TBills with fiat money).
First thing to understand is that the Federal Reserve is not part of the US Government. It is in fact a private corporation created in 1913 by the Federal Reserve Act. The Fed is run by a Chairman (appointed by the President), a Board of Governors (12 of them, appointed for 14 years by the President and confirmed by the Senate) and the Federal Open Market Committee. The Fed is divided into 12 Federal Reserve District Banks that are, in turn, structured like corporations.
So, while the Chairman and Governers are appointed by the President, approved by the Senate and "supervised" by Congress the Fed works like a private corporation and has no direct relationship to the Federal Government. Which means that we have a private corporation setting interest rates, monetary policy and "printing money" to buy our Federal debt.
With regard to printing money, the U S Treasury controls printing of actual money. Printing is done by a contract company. However, that is not how money is "created" or the deficit supported. That is performed by the Fed performing something called "discount window lending" in which a Federal Reserve Bank replaces actual money on deposit by a member bank (reserves) with a place holder. That allows the bank to lend more money to corporations and the public. The Fed also uses something called "Federal Reserves" which they use to buy TBills. The "Federal Reserves" are magic binary money thingies that don't really exist but can be transferred around within the banking system
So
- Where does the money come from? The Fed creates "Federal Reserves" and buys the debt with same
- How is the expenditure showed in the budget? It isn't, because the District Banks are not a part of the Federal Government.
Yeah, pretty darned nifty!