This very interesting article from Saeed Zaman concluding that absent the existence of the zero lower bound economic conditions would have dictated that the Fed set its policy interest rate as low as -5% also contains a useful summary of what I think is a bit of somewhat misguided conventional wisdom about how monetary policy works:
Monetary policy affects the real economy because the level of the federal funds rate sets the opportunity cost for additional funds for banks. The cost of these funds then influences the level of interest rates that banks charge customers for loans, as well as the level of other market interest rates. Higher interest rates (all other things the same) raise the cost of borrowing and tend to reduce loan and investment activity, whereas lower interest rates (all other things the same) reduce the cost of borrowing and tend to increase loan and investment activity.
You will find this in some textbooks, but it doesn't make a ton of sense. For one thing, as our heterodox friends are fond of pointing out this is not a good description of how banks actually operate. In practice, they make the loans they think are going to be profitable and then go get the funds they need to cover the loans. The "pull" of demand for money in the real economy drives the banking system, in other words, rather than a banking "push" driving the real economy.
More generally, the relationship between monetary policy and interest rates isn't nearly as simple as "low interest rates equal easy money." Interest rates have been much lower over the past five years than they were in the second half of the 1970s, but it's perverse to say that monetary policy's been looser during a period of profound recession than high and rising inflation. Today's across the board low interest rates reflect the depressed economy, while the high interest rates of yore reflected the high inflation of the era.
I think it's much more accurate to say that monetary policy works by coordinating expectations.
When you shift expectations to an equilibrium of high expected nominal growth, banks lend more to meet the higher demand for loans. When you shift nominal expectations downward, the reverse happens. The Federal Funds Rate is important primarily as a kind of convention. The Fed has to do something to accompany its announcements, but that doesn't have to be the thing they do. You could always do monetary policy through QE-type large-scale asset purchases or through helicopter drops or changing the Interest on Excess Reserve or required reserve ratios or any number of other things. Interest rate targeting had a good run because everyone understood the convention, but the combination of low inflation and population aging means that negative demand shocks are now going to regularly put us at-or-near the zero bound. That means we'd be well-served to find some other monetary routine to appeal to.