This is my understanding, picked up from a variety of sources - some comparative politics, documentaries, the Tin Drum. Happy for someone with more knowledge to come and correct me. edit: this is mostly about West Germany, though parts of it will apply to East as well.

The general feeling in post-WW2 Germany was to try and forget about the recent past. This culture that was not challenged until the 60s.

One of the best ways to make a militaristic regime look bad is for it to lose a war. The war that was meant to prove German superiority was certainly disastrous for Germany. The figureheads of the Nazi regime were dead or on trial - particularly important for a centralised and highly personalised regime. The death camps revealed the Nazi regime to be even more terrible than many imagined, or at least than many wanted to face up to.

It's also probably not insignificant that many Nazis were simply killed in the course of the war. I would assume that enthusiastic Nazis were more likely to sign up for the military earlier and were thus more likely to be killed.

On a practical note, West Germany under allied occupation went through a process of de-Nazification, that is, the removal of Nazis from prominent positions. (The same thing started in Japan but was not carried through.) There were other obvious reasons to play down Nazi affiliations in occupied Germany.

In the meantime, German and Allied politicians constructed what's I've seen called "aggressive democracy" in the country. The German constitution doesn't just make the country democratic but tries to strongly guard against anything that might change this. So even today, Nazi symbols are widely banned in Germany.

I also think that despite the years of Nazi rule, there was a social democratic and a centrist christian current in Germany that created a base for the country to be rebuilt on. This meant there was not a political vacuum or instability that neo-Nazis could exploit. The performance of the German economy after the war must also have helped.

The continuing threat from the Soviet Union gave an incentive to the right-wing to work with the Western powers to defend Germany. Conveniently, former Nazis in West Germany could keep Communism as their great enemy, while working with the new order in Germany and Western Europe.

Final point is that Nazism continues to have an attraction to an unfortunate number of people in Germany. It never fully went away.