Militarily, the early stages of World War II witnessed staggering German successes. The Wehrmacht rumbled through Poland, Holland, Belgium, and France with frightening speed and efficiency, quickly destroying opposing forces. Only a miraculous seaborne evacuation from Dunkirk in June of 1940 kept a massive British and French force from being completely annihilated. While German efforts to bludgeon Britain into submission with the Luftwaffe in advance of an invasion ultimately failed, when Hitler turned his attention to the East, German armies tore through the Soviet Union, driving deep into Russia itself before the end of the summer. The staggering reverses that would take place later on the Eastern Front seemed very unlikely, and it is well known that the German High Command deemed success so likely that they declined to provide the armies driving toward Moscow with winter gear. So early in the war, German armies swept all before them.
German victories had an enormous human cost. Obviously, the Jews, Communists, and other people deemed enemies of the German state were quickly identified and incarcerated in the West. Hundreds of thousands of Jews, in particular, would be shipped East to the death camps that began to appear in 1942, the year in which most Jews were murdered. On the Eastern Front, the loss of life was staggering, and it was the result of deliberate Nazi policy. Hitler had long hoped to convert the Ukraine, Belarus, and parts of Russia into a massive space for German settlement, and his SS and killing squads, often with the assistance of local collaborators, rounded up Jews, Roma, and Communists for immediate murder, usually by mass shootings, as at the infamous massacre of Jews at Babi Yar, outside Kiev. The Wehrmacht was responsible for the deaths of millions in the first year of the invasion of the USSR, even before the so-called "final solution" was agreed upon. As one historian of Nazi Germany has recently observed, the first year of the German invasion of the Soviet Union resulted in over three million deaths, accounting for a little less than one percent of the population of the planet. Most of these losses were civilians. So the main result of the German invasion on the Eastern front was a staggering loss of innocent human life. All of this was before the Final Solution, Stalingrad, the Soviet counteroffensive, and other massive bloodlettings.
In the early stages of World War II, Germany invaded a number of countries in Western and Northern Europe. Germany used its new tactic of lightning war (blitzkrieg) in these invasions. The invasions were universally successful. The streak of success in land warfare enjoyed by Germany only ended when Germany invaded the Soviet Union in June of 1941. This invasion was the first setback Germany had in land warfare.
The war began with Germany invading Poland. This led to a very swift victory. Nothing really happened in the war from then until April of 1940. At that point, Germany invaded Denmark and Norway. It took Denmark without a fight and Norway very easily as well. Then, in May of 1940, Germany invaded Western Europe. It took Belgium and the Netherlands, and then drove into France. It defeated the combined French and English forces without too much trouble. France surrendered in late June.
The result of these invasions was that there was no opposition to Germany on the continent of Europe. Germany and the Soviets were at peace. Italy was a German ally. Spain was officially neutral but was very sympathetic to Germany. Germany, at that point, dominated all of Europe east of the Soviet Union completely.