Explain how the good times of the 1920s paved the way for the Great Depression of the 1930s.1920s was a time of great economic expansion and...

One way in which the 1920s led to the Great Depression was
by the fact that the boom of the 1920s created a bubble in the stock market.  During the
'20s everything was going (it seemed) so well economically that people thought it would
continue forever.  This led them to borrow in order to speculate in the stock market. 
When the market crashed, people and banks lost their money, helping to cause the
Depression.

You can also argue that the boom times of the
'20s helped encourage the government not to regulate the economy at all.  Because
everything was good, the government just left the economy to function on its own.  As
the link below says,the presidents of the 1920s

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followed a laissez-faire approach.
Laissez-faire refers to the deliberate absence of government
regulation. None of these presidents attempted to regulate the buying or selling of
stocks and bonds; they exercised no controls over banking, manufacturing, or
agricultural production. Likewise, no attempt was made to gather or analyze statistics
that would have pointed to increasing problems in stock investing and overproduction of
agricultural products and consumer goods. This approach to government was a major
contributing factor in the Great
Depression.

By this way of
thinking, the boom of the '20s led to an excessive faith in the market.  This excessive
faith helped lead to the Depression.  (Please note, however, that this is a liberal
argument and that conservatives would generally disagree.)