The Communist Revolution in Russia caused it to withdraw from the fighting and rush a peace agreement with Germany in 1917.
Following World War I, the Allies (England, France and U.S.) disagreed on how to restore peace in Europe. England and France fought a long, bitter war against the Central Powers (mainly fueled by Germany). When peace talks began, England and France wanted to punish Germany for prolonging this deadly war. The Treaty of Versailles outlined the punishment for Germany:
1. The German Emperor had to abdicate power
2. Germany had to demilitarize (significantly reduce the size of its military)
3. Germany had to take blame for the war
4. Germany had to pay reparations (money) for damage caused by the war.
President Wilson (US) did not agree with the harsh punishment of Germany. The U.S. refused to sign the Treaty of Versailles. Instead, Wilson came up with his own plan for peace after WWI. Wilson's plan, known as the 14 Points, included looking at the causes of WWI and preventing them from happening again. Most important to Wilson was the idea for a League of Nations. The U.S. Senate, however, rejected this idea for fear America would be dragged into future European conflicts. Without U.S. participation the League was ineffective and failed.
The condition of Germany after WWI, coupled with the economic conditions of the 1930's led to the rise of dictators such as Adolf Hitler (Germany) and Benito Mussolini (Italy). When Hitler invaded Poland in 1939, after repeated attempts at appeasement, England and France declared war. Following Vladimir Lenin, Josef Stalin came to power in the Soviet Union. At first, Hitler and Stalin created a Non-Aggression Pact, but when Hitler invades the Soviet Union, the country quickly becomes an enemy in the East.
Following the fall of the Hitler's Germany in 1945, the United States, England and the Soviet Union must decide how best to handle Germany. It was clear that the mistakes that were made in punishing Germany after WWI led us to another global war. The Cold War developed in the disagreements between the United States and the Soviet Union because of the fundamental differences between the two countries and the competition of influence on other nations as the only "super powers" after WWII. This competition will continue over a period of more than 40 years and lead the U.S. and the Soviet Union to the brink of nuclear war.
One way in which WWI helped create the tensions that led to the Cold War was by bringing about WWII. WWI, and the Treaty of Versailles that came out of it, angered Germany and made that country want to get revenge on the Allies that had defeated it. This led to WWII, which in turn led to greater conflict between the US and the Soviets.
However, the most important thing that WWI did was to help create the Soviet Union and to make that country distrust the West. WWI led to the collapse of Russia. Russia was so weakened that the Russian Revolution, and then the Bolshevik Revolution occurred. Without WWI, arguably, there would have been no communist country with a great deal of power in Eastern Europe to be part of the Cold War. In addition, WWI helped make the Soviets distrust the West. After WWI, the West sent troops to help the White Russians fight against the communists in the Russian Civil War. This showed the Bolsheviks that the West was hostile to them and it made them dislike the West. This tension would continue and would be the basis of the Cold War.