How did the german and japanese actions lead to the outbreak of war in europe and asia?

Germany extended its territory in Europe because the Germans needed "living space" ("Lebensraum"), they claimed.  They annexed the Sudetenland, then took all of Czechoslovakia, then invaded Poland.  These actions eventually (with the invasion of Poland) caused other nations of Europe to respond with declarations of war.

Japan's imperial aggression in the Far East was similar.  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.