Outside of the technological edge given them by knowing they would be fighting a war soon, and the single minded determination of their leadership to pour billions of marks into developing new and better weapons, there was the fact that the Germans had plenty of time to train up. Again, starting about 1936, the German forces went into high gear in terms of training. Lastly, and perhaps not nearly as important as the other mentioned issues, was the fact that the Germans have a pretty good history of making war and of winning. They had a proud military heritage, and their nation had been humiliated (they felt) and mistreated by the West after WWI, so they were eager to do well. The German Army also had an edge in tactics. Alone at the start of the war, the German high command had fully embraced the possibilities of the weapons which had emerged during World War I. The tactical strike aircraft and the tank, for example, could be wedded together, and the tanks concentrated in large formations as armored spearheads. This was radical thinking. People often forget that the French had more tanks, and technologically superior tanks to the germans at the start of WWII, but had made the mistake of seeing tanks (like the British did, too) as a sort of moving pillbox to support infantry with. As such, their tanks were scattered in "penny packets" throughout their army, rather than concentrated in a few large, powerful armored divisions. It was the genius of Rommel and Guderian to see that concentrating the tanks in large formations, and then supporting them with Stuka dive bombers would allow the tanks to smash through enemy forces faster than they could react.
However, it's worth noting that it didn't take very long, actually, for the British, and then American forces to catch up, in terms of proficiency. Although the Germans kept a technological edge in some areas throughout the war, once those veterans of the first years were killed off, the skill and fighting capacity of the average German soldier wasn't really any better than that of the average American, British or Soviet soldier. The British, Soviet and American forces caught on quickly, and all three soon developed similar tactics, with similar successful results. In fact, the Americans and British improved on the Blitzkrieg tactics, in fact, by motorizing infantry and artillery and linking them to the tank / tactical aircraft team, so that the entire combined arms weight could be brought to bear. Even late in the war, German infantry mostly moved on foot, and German artillery was still mostly horse drawn.