How did international political events combine with postwar domestic life in the U.S. to lead to the mounting hysteria associated with the Red Scare?
Okay, sorry about that. So for the WWI one, here goes:
The major thing that was going on in international politics was the Russian Revolution. In 1917, Russia had become communist, becoming the Soviet Union. There were communist parties in other countries and Americans feared the spread of the ideology.
Domestically, there was a lot of class conflict going on -- there were many strikes going on across the nation, notably the Seattle General Strike and the Boston Police Strike.
Another major event was the bombing campaign that targeted, among others, Attorney General Palmer and led to the Palmer Raids.
So, the communist revolution in Russia, combined with labor unrest and some violent anarchist actions (see also Sacco and Vanzetti) combined to cause the first Red Scare.
I'm assuming you're talking about the Red Scare after WWII and not the one after WWI.
Some of the important international political events:
The USSR taking over Eastern Europe and imposing communist rule on those countries.
The USSR getting the ability to produce nuclear weapons.
China becoming a communist country.
The blockade of Berlin by the USSR, leading to the Berlin Airlift.
The Korean War, in which communist North Korea attacked non-communist South Korea. China later entered the war as well.
These are the main events that convinced many Americans that communism was on the rise and would become a problem within the US as well.