Answer: With Germany's invasion of Poland in 1939.
Context:
As Germany began to seek more territory -- more "living space" for the German people, as Adolph Hitler described it -- other nations of Europe at first tended to allow his actions. A policy of appeasement was signed by the prime ministers of Britain and France with Hitler in Munich in September, 1938. They accepted Germany's annexation of the Sudentland as a German territory, including the evacuation of any Czech population from the region. Soon after, Germany took over all of Czechoslovakia -- but still the Western powers of Europe were not ready to go to war to stop Germany. It was when Poland was invaded and quickly defeated by German blitzkrieg forces, beginning September 1, 1939, that Britain and France determined it was necessary to go to war with Germany. This is considered the beginning of World War II in Europe.
We might wish to note that the conflicts that became part of World War II actually began earlier than 1939 in the Asian region. Japan invaded the Chinese territory of Manchuria in 1931. Japan's imperial ambitions even reached the point of genocidal acts such as the massacre at Nanking in 1937-1938. In 1940, Germany, Italy and Japan signed the Tripartite Pact, and as a group they became known as the Axis Powers, which fought World War II against the Allied Powers.