They influence creation of money by adjusting the short-term interest rate which influences the demand for borrowing at commercial and retail banks. It's not that direct or straight-forward though, because they only have control over the short end of the yield curve not the long end. The long end of the yield curve has interest rates defined mostly by inflation expectations. If they dropped rates to 0% overnight it probably wouldn't move the 30Y yield all that much -- it might even raise it because of the expectation lower short-end yields would raise inflation.

The Fed doesn't have nearly as much control as folks think.

The Fed directly created money during QE and they are directly destroying it during QT. There's a net add, but that's mostly because the economy is growing, which creates new demand for money as expressed by demand for debt.

The money supply staying fixed or shrinking is a non-goal anyways. It's irrelevant. What matters is inflation as measured from the change in actual prices.

they lie about real inflation, everywhere