I recently read The Coming of the Third Reich by Richard Evans, which is the first of a three volume history on the Nazis.
Evans covers a lot of ground in this book, beginning with the Second Reich (1871--1919) and Bismarck, who was its Chancellor from 1871 to 1890. Bismarck was a dynamic political leader, whose legend loomed over the German psyche during and after WWI. The Germans were a bit upset about losing the war, and humiliated about the war reparations they had to pay after the Treaty of Versailles in 1919. The postwar government was democratic, weak, and chaotic. Many longed for a strong central government with a dynamic leader.
Enter the Nazis in the early 20s. They were just one among many small political groups in the country. The "National Socialist German Workers' Party" were actually on the right side of the political spectrum, although they criticized capitalism as well (hence the Socialist Workers part). They were basically a hate party--they hated capitalism, communism, foreigners, Slavs, Jews, homosexuals, and basically anyone who disagreed with them.
I had read in the past that the Nazis persecuted communists, but I had always assumed that that was because of the national face-off between Stalin and Hitler in the late 30s. But communism had always been a target of the Nazis. There was a real fear that there would be a communist revolution in Germany, like the one in Russia in 1917. The various communist groups all had their paramilitary units, as did most other political groups. The Nazi paramilitaries were called the Brown Shirts, and they would often get into brawls with communist groups. German politics in the 20s and early 30s was almost like gang warfare, where political speeches and rallies ended in fisticuffs, and small-time political assassinations were not uncommon.
The ascension of the Nazis and Hitler in the early 30s was only possible because of the Great Depression. Germans were unhappy with high unemployment and were ready for a change in government. Nazi representatives were voted into the Reichstag (German parliament) in 1932 in large numbers, and in what turned out to be a huge miscalculation, Hitler was appointed chancellor in 1933. It was understood by those who did the appointing that he would be kept in check by Vice Chancellor Franz von Papen, President Hindenburg, and the military. Obviously, that didn't work out so well.
The incident that sparked the Nazis takeover of government was the fire in the Reichstag. On February 27th, 1933 a crazed unemployed communist "insurrectionist" single handedly set fire to the German seat of parliament in the hopes that it was incite a communist revolution. He acted alone. But Hitler and the Nazis proclaimed this to be the planned action of a vast communist conspiracy, and took advantage of the opportunity to purge Germany of communists. This was the beginning of Hitler's dictatorship and the first step in a larger purging that would take on cultural and racial dimensions.