There were a number of ways in which the Depression in the US affected the global economy.
First, there is the aspect of trade. The United States was, of course, one of the richest countries in the world at the time. It was an important player in global trade. With the coming of the Depression, American demand for imports dried up. This was exacerbated by the Smoot-Hawley Tariff. This hurt all the countries that exported to the US. It also encouraged other countries to create trade barriers. This hurt world trade further.
Second, there was the fact that Germany’s economy was heavily dependent on trade and on loans from the United States. With the Depression, the US stopped being able to loan money to Germany. This, along with declines in trade, damaged the Germany economy terribly.
Finally, the Germans were, in those days, paying reparations for WWI to the French and English. When the Depression hit and they could no longer borrow from the US, they stopped paying those reparations. The French and British economies were badly damaged and the Depression spread.
The above answer contains little of substance. In fact, most of the world suffered from the Great Depression, as did the United States. The depression in the United States was actually exacerbated by the failure of a large Austrian Bank. This shook investor's confidence in banks resulting in their purchasing large amounts of gold bullion which in turn caused even greater deflation. Unemployment in Austria reached 29%. In Germany, unemployment reached 30%; unrest in that country was largely responsible for the collapse of the Weimar Republic and the award of dictatorial powers to Adolf Hitler.
The Soviet Union alone managed to avoid the worst of the Great Depression, as Joseph Stalin's policies of collectivization and forced industrialization kept the country's economy functioning at close to normal levels. Its apparent success in avoiding economic collapse was seen as a validation of communism as an economic system and an indictment of capitalism. This led to communist agitation in many other parts of Europe and also in the U.S.
What a great question in view of our current economic climate. Even as far back as 1929, we could see that the economies of the world were somewhat related. In other words, what happened in the United States had an impact in the rest of the world. In view of this point, let me make a few observations.
September 4, 1929 is the day known as Black Tuesday. It is the day that the stock market crashed. From a global perspective this is significant, because it sent ripples to other countries and their stock markets. This shows that the markets even 80 years ago were interrelated in some ways.
Second, on account of this international trade dropped nearly 50%. The implications of this are staggering. Think of the decrease in manufacturing? Any country that manufactured lost tons of jobs. Think of all the jobs related to manufacturing and the implications - oil, shipping, and the like. All of these business were hit hard as well. Jobs were lost and this created a very bad cycle.
Third, agriculture and mining were also hit very hard and these industries were at a standstill. And because banks took a hit, there was little in terms of building, lending, and all new projects were put on halt. Truly this was an international crisis.