They understood that the strongest and most renewable emotion in mankind is fear, and that, once a people have been won over by fear, there's very little that you can't get them to do.
To provide a focus for fear, a demon is necessary. Ideally, the people already fear a demon of some sort. If so, this demon should be co-opted and the fear magnified.
However, if no demon is already perceived by the people, one must be created.
The Nazis chose existing demons. Many Germans had an existing fear and hatred for Jews, non-whites and homosexuals, so the Nazis did all they could to demonise them and to present themselves as the crusaders against these demons.
Once this relationship has been created – that the only way to be saved from the demons is for the government to defeat them – the rest is actually quite simple. The creation of a police state, the banning of publicly held weapons, the pogroms, the waging of war, all of it can be accomplished by describing them as necessary in the defeat of the demons.