The two events that led to the outbreak of World War II in Europe and the Pacific were, respectively, the German invasion of Poland and the Japanese attack on the United States naval base at Pearl Harbor, Hawaii.
By 1939, Adolf Hitler's Germany had already remilitarized the Rhineland, annexed Austria, and taken all of Czechoslovakia. Hitler had secured Czechoslovakia despite promises made to British Prime Minister Neville Chamberlain at the Munich Conference, held in response to a crisis in the region. This action, in addition to the Nazi-Soviet Non-Aggression Pact later in the year, sobered the British and French, who had hoped to play Hitler and Stalin off each other. They committed to come to Poland's aid if it was attacked, and when Hitler launched his blitzkrieg invasion in September of 1939, World War II began.
By 1941, Japan hoped to expand into Dutch Indonesia, which had much-needed oil, a commodity which the Japanese islands completely lacked. In the summer of that year, they moved troops into French Indochina, and the United States government retaliated by declaring an economic embargo against Japan, which cut them off from a valuable supplier of oil. If the Japanese were to continue fighting in China and expand throughout the region, they had to either secure good relation with the US or to invade Indochina. Conceiving that the first option was impossible, the Japanese High Command launched a surprise attack against the US naval base at Pearl Harbor. The United States subsequently declared war.