As fear of communism specifically, but radicals in general, grew after World War I, the potential for a Red Scare overreaction grew along with it. There had been many, many recent immigrants to America, and many carried with them some radical ideas, especially anarchy.
Attorney General A. Mitchell Palmer, his own home attacked by a radical, conducted the Palmer Raids in 1919 and 1920, arresting several thousands suspects (most of them innocent) and deporting about 500 of them. People with Russian last names were a common target, as we suspected that they had brought communist ideas to the US, or were working as communist agents. We deported them back to Russia where many were arrested and killed.
A piece of trivia for you - One of Palmer's right hand men during the First Red Scare was one J. Edgar Hoover, later FBI Director during the Second Red Scare and the Justice Department in Washington DC still bears his name.
The conclusion to the First World War, where Communism enveloped Russia caused a great deal of fear in America. This was linked to the fear of Europe, in general, during and after the First World War. In addition to this, many in America were advocating Communist, or Marxist ideals, as a response to Capitalism. The fear of what was happening in Europe as well as the ideas that others in America were discussing led to a reactionary fear of expressing viewpoints that could be seen as Communist. The case of Sacco and Vanzetti represented one moment where individuals perceived to be different were subject to court proceedings where evidence was not very strong, and fear dominated all else, as well as the death penalty. In the end, the Red Scare proved how the promises of a nation predicated upon freedom of expression and thought could be betrayed by its reality.
This first red scare in American history probably started with the Russian Revolution of 1917. This revolution essentially created the world's first communist country.
In the United States at that time, there were many communists and other radicals, many of them immigrants. Americans were worried that they would be inspired by the Russian Revolution. This seemed to be coming true in 1919 as things like the Seattle General Strike and the attempted bombing of the Attorney General of the US happened. At the same time, the Soviets had had a meeting of the Comintern, which was meant to spread communism throughout the world that year.
So these foreign events seemed to be driving communism in America and this helped lead to the Red Scare.