How did the use of Article 48 (of the Weimar Republic's constitution) help Hitler's rise to power?
Article 48 of the Weimar constitution authorizes the President to assume certain powers when faced with a state emergency:
In case public safety is seriously threatened or disturbed, the Reich President may take the measures necessary to reestablish law and order, if necessary by force.
In particular, the President could suspend civil liberties and rights, including due process rights. The article was designed to prevent a revolution such as the one that occurred in Russia that led to the establishment of a communist state. But Hitler, once elected Chancellor, was able to cynically exploit the provision. (The President, von Hindenburg, essentially signed off on Hitler's actions.) Claiming that the state faced the specter of a Bolshevik revolution, he used Article 48 to justify the overthrow of the elected Prussian government as well as a series of raids on Communist leaders (as well as a few of his own rivals.) After the Reichstag fire of Feburary 1933, Hitler invoked Article 48 again, claiming the power to run the government essentially by decree. The Reichstag passed enabling legislation that allowed Hitler to impose dictatorial rule on Germany. When von Hindenburg died in 1934, Hitler was able to further consolidate his power, which he continued to claim (at least while such claims were still useful) was based on the Weimar Constitution.
Article 48 of the Weimar Constitution allowed the President of Germany to claim emergency powers without the agreement of the Reichstag (the legislative branch of the government). After Hitler was elected on January 30, 1933, the Reichstag caught fire on February 27. Hitler claimed that the fire was the work of Communists and convinced Hindenburg, then the German President, to invoke the emergency powers granted by Article 48. Under the emergency decree, the government suspended the right of free speech and assembly, the right of habeas corpus, and other rights. The suspension of these rights allowed the Nazi Party to crack down on dissent and eliminate their opposition (the Communists) en route to forming a dictatorship. After the elections held on March 5, 1933, the Nazis passed the Enabling Act, which gave the German Cabinet (which was in effect simply Hitler, the Chancellor) the power to pass laws without the Reichstag. Article 48 was the basis on which Hitler claimed he had constitutional authority to become a dictator.