This is a good question, and it's a shame that others don't think so.
I'd recommend the book Rainbow's End: The Crash of 1929 by Maury Klein. It's part of the Oxford University Press series "Pivotal Moments in American History," and it's well-cited, readable and has been printed enough to be easily accessible. Klein does a really good job of distinguishing the difference between the crash itself and the Great Depression, which are really two different events, though closely related.
You might also try The Ordeal of the Presidency: Herbert Hoover in the White House, which isn't as good of a book but does go into the decisions being made as the crash took place.
During the 1920s, the United States enjoyed a long and productive boom in most sectors of the economy (with the exception of agriculture, perhaps). This meant that many Americans had extra cash in a way they didn't before.
During the 1920s, there were many new consumer products to draw some of that cash, but in the second half of the decade, there arose a belief that every American could become a millionaire. The boom had been going on for so long and with such force that it didn't seem impossible.
Books like New Levels in the Stock Market, by Ohio State Professor Charles Amos Dice, put forward the idea that the United States had entered a "new economy" whereby stocks would permanently increase. Irving Fisher famously predicted in the fall of 1929 that "Stocks have reached what looks like a permanently high plateau. ... I expect to see the stock market a good deal higher than it is today within a few months."
With almost everyone predicting that the good times would continue (or even accelerate), ordinary Americans wanted to be part of the game. They invested in the stock markets as they had never done before. The spread of telecommunications meant they had access to those markets, and mass advertising encouraged them to invest.
In addition to investing their savings, many Americans even went so far as to take out loans to buy stock. If you presumed that stocks would inevitably rise, it was a saavy move. You could borrow money, buy stock, and quickly pay off the loan by selling a portion of the stock you'd bought. You'd still have some of the stock, leaving you with more money than you had before.
When the crash occurred, it had three significant implications: It wiped out the savings of many small investors, it crippled the banks that had loaned money to stock-market speculators, and it made many Americans reluctant to borrow money, invest, or spend.
By wiping out Americans' savings, the market crash reduced their ability to buy non-essential products: a new car, a new house, a refrigerator instead of an icebox, or simply toys for the kids. This harmed producers and retailers.
Banks that had lost millions on defaulted loans were on shaky ground. Some, particularly in Detroit, collapsed, and people who had kept their money in the bank instead of the market lost their savings. Furthermore, banks became much more reluctant to loan money to businesses interested in expansion, new homeowners, and other purchasers. This further reduced economic demand.
With all of these factors in play, people became much more conservative about how they spent their money, particularly as the job losses started adding up. This harmed the economy as a whole. Without people buying products, there was less need for people to make products. There was less need for people to mine the minerals needed for those products.
Each layoff exacerbated the problem, increasing the difficulty of recovery and increasing the chances of further foreclosures leading to further bank failures and deepening the cycle. The problem created by the crash was a shortage of money flowing through the system. It was a stroke, a blockage of the blood supply, and while not fatal, it had debilitating effects on the global economy.