How did WWI and it's aftermath contribute to the rise of fascism in Europe in the 1920's?

The end of the First World War was marked by the signing of the Treaty of Versailles, a product of negotiations between Britain, France, and the United States. The ostensive aim was to create a stable Europe unlikely to fall into another great war. The effect, however, was to punish Germany for its role in inciting the conflict and to extract harsh reparations. In addition to monetary reparations, Germany was to give up its military, relinquish territory, and surrender its colonial holdings.
Following the treaty, Germany became engulfed in an economic collapse which brought about shortages, crippling inflation, and a popular dissatisfaction with the Weimar government. Hitler rose to power in this climate because he promised a reborn, powerful Germany able to take revenge on France and Britain. Under Hitler, masses of unemployed men were conscripted into a quasi-military force tasked with the construction of a civilian infrastructure capable of serving a new German military.
Hitler’s brand of nationalism proved compelling enough to propel him to the chancellorship in 1933. In the aftermath of Hitler's rise to power, democratic institutions were overturned and, ethnic minorities especially jews were singled out for persecution. Hitler mobilized the population by asserting that German jews were responsible for the nation’s economic collapse, the rise of communism and all other problems past and present. By the late thirties, Jewish businesses were being burned or boycotted; and as the forties progressed Jewish families were sent to ghettos and eventually to concentration camps for systematic execution.
Though Hitler’s rise to power was especially alarming, Italy’s Benito Mussolini established the first fascist regime in 1919. Much like Hitler, Mussolini rose to power in the economic turmoil that followed WWI by promising to end to mass unemployment and to create a reinvigorated nation capable of imposing its will on its neighbors.
In the early 1920s Mussolini formed squads of followers, called “Blackshirts” to terrorize political opponents like socialists and communists. The communist revolution in Russia had taken place in 1917 and Mussolini’s fascist movement quickly gained the support of anti-communist business people, property owners, and middle-class workers. By 1922, Mussolini had become so popular that leaders in Rome could do little to halt his ascension to all-out dictatorship.

References
Ambrose, Stephen (1997). American Heritage New History of World War II (2nd Edition): Viking Press.
Shirer, William, L. (1960) The Rise and Fall of the Third Reich: A History of Nazi Germany Reissue Edition (October 11, 2011): Simon & Schuster

It is particularly the aftermath of WWI and the Treaty of Versailles that contributed to the rise of fascism in Europe. Italy's frustrations over their role in the treaty negotiations led to a government crisis and the eventual rise of Benito Mussolini a few years later.
The central issue with Versailles, however, was the treatment of Germany. The Germans were forced to admit to being solely responsible for the losses of the war. War reparations were severe and led to hyperinflation and the near collapse of the German economy in the 1920s. In the chaos of this period, many of the traditional elements of the German power structure came to be questioned. Radicalism and antisemitism thrived and nationalism grew. Key pieces of German territory, like the Ruhr Valley with its valuable coal mines, were taken out of the country's hands. Germany was also prevented from having all but the most minimal military force.
Out of this crucible arose German fascism. Hitler came to power with promises to restore German strength and sovereignty, regain lost territories (and acquire new ones), and rebuild Germany's military greatness. All this led to the outbreak of World War II.