How the Holocaust Came to Happen

There were many causes of the holocaust and they were much more complex. Radicalisation is often the result of crisis, and then was no different. The number of votes the Nazis got was reflected precisely by the rate of unemployment: it meant people were getting desperate and felt like they had to take desperate measures.
Germany was the country hardest hit by the Great Depression of any country in the Western world, what with the aftermath of hyperinflation caused by their debt to the Treaty of Versailles. Because of this treaty, it was easy for the Germans to blame the West entirely for the state of their economy, so when the Nazis promised to stand up to the West, they got 1/3rd of the population on board.
Far-right movements anywhere are associated with racism, which nowadays we see mostly in the form of anti-immigration. It's part of the xenophobic fight-or-flight response that drives radicalisation. The Germans probably didn't care as much about racial supremacy as about getting anyone who didn't belong to their group out, out of fear that they would turn against them.
When Hitler began his campaign of antisemitism, there was a particular reason why he was so successful: centuries earlier, the Church had forced Jews into the profession of bankers because it's forbidden for Christians to charge interests on loans, making banking impracticable (because the money will eventually be lost from defaults). This made the Jews disproportionately wealthy (the USA, they still form between a quarter and a third of millionaires), especially in Germany. So instead of blaming a broken system, the people blamed the Jews for being rich much as people blamed the top 1% in the Recession, except this was in a far more dire situation were people were starving by the thousands from poverty and everyone was terrified of suffering the same fate.
Once WWII began and all the able-bodied men were at the front, Hitler's totalitarian power made it easy to start carrying out the holocaust behind the people's back, since he controlled the press. While it's certain that the people heard rumours, by then they were too busy with WWII to worry about them and hoped they were just slander, but even if they weren't, revolting against Hitler would mean losing the war, which they thought would lead them through another hyperinflation. Because the country was at war, the guards of the concentration camps knew that any disobedience would be seen as high treason and met with severe punishment, so they rationalised that if they didn't do it, someone else would just do it in their place: they were just a cog in a machine and "had no choice" but to do what they're told.
The Nazis are a sad story of what happens when, rather than trusting your conscience for guidance, you turn to people in authority to save you from your fears. People are very weak, and Milgram's experiment shows that this goes for all nationalities. As long as we don't seek for our own values, we will be susceptible to radicalisation. Ironically, if people had actually listened to Nietzsche, the Nazis would've therefore never risen to power.