During the mid to late 20s the Fed's expansionary credit policies drove up stock prices and kept other prices higher than they should have been. During the 20s we were an incredibly productive country, which means consumer prices should have been falling, but the Fed made sure they didn't. That is the same thing as typical price inflation that people recognize.
When the bubble in the stock market burst, all of that easy credit disappeared as bad firms failed. That wasn't a result of tight policies by the Fed, that is reality when businesses propped up by the bubble mania burst, because they were the ones using up a lot of the Fed's easy credit. The Fed did everything they could to keep inflating, but the gold standard did put a check on them, thankfully. At least until FDR took us off the gold standard and stole the gold from the American people.
Anyway, without an inflating bubble to drive up prices, obviously stock prices fell to where they should have been, and consumer prices tried to fall to where they should have been (until the government stepped in with subsidies and wage controls and what have you.)
You can see today, without a gold standard, what they wanted to do. The Fed has printed untold trillions to try to prop up housing prices. The problem is, they can't stop that correction without destroying the purchasing power of our money. Housing prices are too high. There isn't demand for these homes at these prices. Housing prices will never again rise until they are allowed to fall to their bottom, unless the destruction done to the dollar is irreparable and the prices of everything are skyrocketing.
If the government would have minded their own business, prices would have bottomed out, nominal wages would have fallen, unemployment wouldn't have risen anywhere near the levels it did, and by 1932 the economy would have been growing again. Instead, Hoover decided to spend on massive public works, outbidding private companies for labor, and driving up wages. He also held meetings with the biggest companies, begging them not to cut wages. This, of course, prices millions and millions of people out of jobs. Because prices were crashing, that means real wages were skyrocketing, so people who had jobs and frozen wages were in effect getting huge raises, but that meant companies couldn't employ as many of them. The government also subsidized farmers and paid them to destroy crops to try and prop up food prices, which as you might expect, led to widespread starvation. The terrible times during the depression that they put in the history books were caused by government intervention.
If we weren't on a gold standard, the Fed would have printed a lot more, but it wouldn't have changed anything. They would have propped up consumer prices with this extra inflation, which means unemployment might not have been as high, but then the suffering would have been enjoyed by everyone, even those who were working. The economy would have been stagnant as long as the government put off the correction, just like today.
When people say World War II finally ended the Depression, I think they are partially right, but for different reasons. Obviously the idea that printing and borrowing a bunch of money to build tanks and blow them up and shipping tens of millions of our most productive workers overseas to get shot being an economic stimulus is ridiculous. What World War II did though was bring the correction that the government wouldn't allow. Everything was rationed, all people could do was save their money. After four years of austerity, the budget was cut in half and ten million people came home and found work without public works programs and wage mandates. All they had to do allow the correction to happen and people to save their money and all of a sudden there was real saved capital available for businesses and the economy grew again. If they would have allowed that austerity to take place in 1929, by 1931 or 1932 the economy would have been moving again, and there would be no such episode known as the Great Depression.