To understand the role of the Federal Reserve in the causation of the current depression, we must understand its influence on interest rates, and how interest rates influence economic activity.
The Treasury Department borrows money to finance government activities by issuing bonds, which are bought by banks and other investors, and also by the Federal Reserve. When the Fed wants to stimulate economic activity, it buys Treasury bonds from banks and other investors, paying cash, which increases the balances in bank accounts and by doing so provides more money for lending and spending. (The process is actually somewhat different and more complicated, but I am presenting an intuitive version that will be easier for readers who are not experts to understand.) As the supply of money for loans rises, interest rates fall (the larger the supply of a good, including loans, the lower the price, which in the case of a loan is the interest rate). As interest rates fall, borrowing becomes cheaper, and people borrow more and go deeper into debt, rather than saving. With more borrowing, banks need more money to lend, so they borrow too; as it is cheaper to borrow capital than to raise it by issuing more stock (because interest is deductible from income tax and the compensation that providers of equity capital to firms receive from those firms is not) banks become more indebted too, and hence more risky. And because houses are a product bought mainly with debt (for example, an 80 percent or 90 percent or even 100 percent mortgage), the demand for houses rise. So more houses are built, but in addition, because the overall stock of housing is so durable and is therefore not replaced frequently, the increase in demand pushes up prices. If nothing else besides low interest rates is pushing up housing prices, we have a bubble, in the sense that, as soon as the crutch of low interest rates is withdrawn, prices are likely to fall, as houses become more expensive to buy, the higher interest rates are. It was the collapse of the housing bubble when interest rates rose (mainly in 2005 and 2006) that started the economic collapse, and because banks were so heavily invested in housing through their role in issuing mortgages, they came near to collapse as well, triggering the depression.
The Federal Reserve pushed interest rates way down at the end of 2000 and kept them there until 2005 and during this period of low interest rates (in part of the period, the short-term interest was negative in real terms, because it was lower than the inflation rate). This was the decisive error that put too much risk into the economy, against a background of deregulation that allowed the banking industry to take whatever level of risk was profit maximizing given interest rates. The Fed was fooled by the fact that the usual indices of inflation, such as the Consumer Price Index, did not indicate a high rate of inflation. But the reason was that low-cost imports from China and other East Asian countries kept prices of most goods and services down. Inflationary pressures caused by an overheated economy flooded with lending were deflected into assets such as houses and common stocks.