How Did Hitler conquer so much of Europe in such a short period?
There were two main ways in which Hitler (and the German military, which actually did the conquering) was able to conquer so much of Europe so quickly.
First, Hitler and Germany were much more prepared to go to war than any other European country. Since Hitler had come to power, Germany had been rebuilding its military with the clear purpose of one day going to war. By contrast, most other European countries had been hoping that war would not arise again. The French and the British, for example, simply did not have their armies built and trained with the assumption that they would be going to war. They felt that things like the Treaty of Versailles and the Maginot Line would prevent war.
Second, Hitler and Germany had better tactics. The French and the British had not really updated their tactical thinking since World War I. They had not thought much about how things like motor vehicles and airplanes could be used to create a style of “lightning war” like the Germans had planned out. Between them, these two factors meant that Hitler and Germany were much more prepared to wage an effective war than any of the countries they went up against.
Hitler was able to conquer so much of Europe in a short period of time because the rest of Europe was unprepared. The rest of Europe spent a smaller percentage of their money on the military compared to Germany. The Versailles Treaty and further disarmament conferences were supposed to have made war unlikely if not impossible. France thought their series of forts, the Maginot Line, would prevent any further invasion, but they did not account for the advances of military airplanes between the wars. One cannot entirely blame the leadership of these countries for not bolstering their armed forces--after WWI, many people were sick of war and would do almost anything to avoid the possibility of another one.
Hitler also integrated his mechanized units with his infantry. This blitzkrieg made war in the trenches unlikely. By emphasizing a war of movement, Hitler avoided the trap that many military planners make: fighting the last war. Hitler's modern forces proved to be invincible in the open spaces of Eastern France and Poland. It was only when they encountered the urban warfare of Stalingrad that the German forces realized their limitations.