It's a very common misconception that the Nazis democratically came to power in Weimar Germany. Besides the regular everyday street violence they conducted with their brownshirts, president Hindenburg had been ignoring the parliament and setting up his own government via presidential decree for some time. Prussia (a social-democrat stronghold) had been illegally overtaken in a coup by the then chancellor Franz von Papen.

The only reason Hitler became chancellor is because of the internal squabbles the conservatives around Hindenburg had, and the compromise they agreed upon was to give (again via presidential decree, the parliament was absolutely irrelevant) Hitler the chancellorship and the police, since they thought that he was an inexperienced fool they could easily handle.

With the police in his hands, the SA could start killing, looting and burning places belonging to their political opponents without any worries. After the Reichstag fire, the socialists (2nd biggest party) and the communists (3rd biggest party) were were being murdered and arrested in such quantities, they had to open up concentration camps just to have a place where to put them. The election campaign of 1933 was a symphony of Nazi violence, and they still didn't have a majority in the Reichstag. It took a lot of threats, violence, backroom deals and the support of Hindenburg for the Nazis to get the enabling act through the Reichstag, after which they were essentially the law.

The Nazi seizure of power was everything except democratic. The courts, people and most parties were against democracy to begin with, but by the time the Nazis had any real "legal" power, the voice of the people was absolutely irrelevant since the president could and did rule by decree, bypassing the Reichstag, and even outright illegal actions such as the coup in Prussia was just brushed over by the courts stacked with conservative judges who've been there since Bismarck.