Early German successes can be attributed to their strategy of Blitzkrieg, which means "lightning war". Hitler began with a conquest of Poland in 1939 that turned out to be surprisingly quick. Germany basically committed all of its combat troops and planes to the invasion. Well-coordinated attacks by German tanks and armored vehicles, supported by superior air power, destroyed the big, but slow, Polish army. German infantry still moved on foot or horse, but they had a disciplined advance and picked up after the devastating things the tanks had done. The Poles fought hard, but they were so shocked and disorganized, there was little hope of mounting a successful defense. This was what the German officer corps had trained for: Blitzkrieg. Within three weeks, German troops were laying siege to Warsaw and Poland was dismembered in four weeks.
In spring of 1940, the Germans started at it again. They struck first in Scandinavia, took Denmark in a day, and invaded Norway. In May, German forces swarmed through Belgium and the Netherlands on their way to France. The two nations were conquered shortly after one another. When the Dutch succeeded in flooding canals that protected their major cities and defended themselves with their marines, Hitler ordered his air force to bomb Rotterdam. More than 800 Dutch civilians died, and the Netherlands surrendered the day after.
The large French army that the Germans faced were carved up by the Blitzkrieg. Its divisions were isolated and overwhelmed by German aircraft, which were working to an exact plan. French units either fought fiercely until they were hopelessly surrounded or they just collapsed. Poor organization on the French's part turned out to be, once again, a detrimental trait.
The Germans' precision, organization, and speed covered in their Blitzkrieg ensured their early successes.