Bear with me, because I'm going to start with global economics. The Great Depression impacted not just the US, but countries spread across North America, Europe, Asia, Australia and Africa. This heavily covered impacted trade and resulted in high tariffs and a 30% reduction in global trade between 1929 and 1939.
The political results were many. Germany and Italy fell under fascist rule. Argentina had a military dictatorship. Other countries also experience political upheavals. Because countries were unable to purchase raw materials and commodities such as coffee, rubber and tin, export revenue dropped significantly. Unemployment rates skyrocketed, the effect of which was civil unrest. That is the condition that enabled the takeover by dictators, the Nazis and others.
Let's look at Germany. Hitler's plan was to repair and bolster the German economy by getting rid of unions and replacing them with industrial cartels (more about cartels in this book. He also stepped up militarization, which significantly lowered unemployment and bolstered the military.
Italy's Mussolini gained strength as a result of the unrest although his government was already in power.
Japan invaded Manchuria after becoming militarized during the 30s, a move that gave Japan access to China's resources as well as their coastline.
Now, we must consider Stalin and the USSR. Stalin's 5-year plan was underway in 1928 and was a policy of collectivism where peasant farmers basically gave their agricultural products to the government for pennies. He also stepped up industrialization. During the depression, millions were killed or sent to Siberian camps which further tightened Stalin's grip over the population and forced conformity to his plan.
In Europe and the Canada, welfare capitalism became the standard and the government took responsibility for removing the risks of bankruptcy and unemployment by attempting equal distribution of wealth and power.
In the US, the political climate changed significantly, giving the support of ethnic groups in cities to interventionist politics. Programs such as pensions, unemployment compensation and welfare payments were developed. The FDIC was established to protect bank deposits and the stock market was more closely regulated than before.
Overall, the global political climate changed quite significantly during the Great Depression in response to the crashes economies of countries around the world.
Here are some resources