The process of 'money creation' is basically a pyramid, with the Federal Reserve at the top, the Commercial banks below, other lenders, such as Investment Banks and S&L's below that.
Each of these entities create more 'money' by Lending. Only a small fraction of the money in circulation is represented by cash, i.e. greenbacks. The Lending activities the banks can do are restricted and regulated by several mechanisms-
1- Reserve requirements. For every dollar you lend, you must have a certain fraction deposited with the Fed. One easy way to curtail lending (i.e. growth in money supply) is increasing minimum reserve requirements. Or lowering the interest rate you pay on those reserves. Also asset base requirements- for every dollar you lend, you must have a certain minimum liquid asset base, that is a minimum fraction of those loans outstanding. This can be varied too.
2- Open market activities- this is the most transparent of the Fed's operations. To increase liquidity, buy T Bonds and inject cash into the economy. The Fed collects the interest, the sellers are paid out for their bonds. Reduce liquidity- Fed sells bonds. The buyers pay out cash for their future interest payments, the Fed takes the cash out of the economy. Buyers hard to come by? Simple- increase the interest rates. The Fed basically controls the interest rates, in consultation with the US Treasury. Historically, this was only ever done with AAA+ US Treasury Bonds. Now, the Fed is buying, and Lending against, Junk. Extremely dangerous.
3- Moral persuasion. If the Fed has a word in your ear, Bankers listen. Otherwise they might increase your reserve requirements, or order a thorough audit on your operations. In that game, you don't argue with the Fed.
4- Cash creation. The Fed has a license to print money, and an effective monopoly on this. I say effective, because it is nowhere enshrined in law. It is under no obligation to disclose this either. Interestingly, President JFK set out to overturn this 'monopoly'. If I recall correctly, some non-Fed bank notes were even printed and issued, soon before he was assassinated. One for the Conspiracy theorists.
The idea died with him, and was quietly buried.