Reading a time line of Nazi Germany, I find it mind boggling how fast the Nazi's moved. Within months of taking power Hitler could make any law he wanted, the gestapo is formed, less than half a year in and there are book burning rallies and rival parties are banned. Perhaps I'm naive but it's hard to believe how fast things changed. I would've have expected it to take some time for the Nazi's consolidate their power not literal months.
It's a combination of political manipulation and fear.
Many people feared Hitler would use a position of power to increase his own dictatorial powers, at home and abroad. To curb this, Papen convinced President Hindenburg to appoint Hitler as Chancellor with the caveat that the Nazis would acquire only three positions in the cabinet, the Chancellorship included, with Papen and other conservatives curbing his ambitions. This was in January 1933. About a month later, the Reichstag (German parliament) was set on fire; some people believe the Nazis perpetrated the arson themselves but, either way, the blame was put on a Dutch Communist. The rising, populist movements during the Weimar period were the Nazis on the extreme-right and the Communists on the extreme-left. You can see this in the election results leading up to January 1933. In the July 1932 election, the Nazis were the highest performing party (albeit without a majority) and the Communists were the third. Even though they remained in the same position during the next election in November, the Nazis had lost 34 seats and the Communists had gained 11. For much of Germany, especially the conservatives and right-wing leaders in the higher echelons of German politics, the Nazis were seen as a more tolerable force. Hitler and the Nazis used this to their advantage. The Reichstag fire was used to stoke fears of a Communist plot being worked up against Germany, so, when the Enabling Act (which effectively gave Hitler dictatorial powers) was suggested, the mostly right-wing parliament voted for it. It was effectively giving parliament the choice between a Nazi with increased powers versus what they perceived to be leniency against Communist revolutionaries. The KPD (Germany's communist party) were prevented from voting by the Nazis and many Social Democrats, the only major party to denounce the act outside the Communists, were threatened from voting. With that, Hitler had more-or-less sealed his dictatorial powers. In effect, if you want to see the downfall of democracy in Germany from this point of view, he was able to do it in a year by stoking fear and manipulating fears of Communism while repressing those against him with violence.
Saying this, there was still a chain of command that outreached Hitler's single-person style of governance after this point in the form of Hindenburg. Hitler was still only the Chancellor and Hindenburg was the President. While ineffective in the long-term, Hindenburg still could and, on occasions, did curb his power. For example, when Jewish people were barred from civil occupation, Hindenburg pressed the exclusion of war veterans. Besides, Hindenburg controlled the army and garnered massive respect as a war hero. He was able to defeat Hitler in the Presidential election and he could dismiss him as Chancellor. It took his death in 1934, more than a year after the Enabling Act, to merge the posts of Chancellor and President and totally gain control over the government.
Most of this comes from Ian Kershaw's Hitler, which I strongly recommend.