Adolph Hitler had German history on his side. An ardent nationalist who fought in World War I, he was shocked by what he and many others considered the "backstab" of Germany's surrender. He quickly became involved in politics and soon rose to the top of his far right-wing National Socialist party because of his skill as an orator.
The time was ripe for a far-right party to emerge. Germany was humiliated and unstable after World War I, with heavy reparations payments, an economy in shambles, and for the first time, a republic (rather than monarchial or princely rule). The republic was hastily patched together to avert a communist takeover and was a shocking concept to many people. Politically, Hitler exploited the chaos and economic distress people suffered, blaming it on the Jews, on the republic (which he claimed was run by Jews), and on the avant-garde (which he claimed was Jewish). He had a ripe audience in people looking for a return to traditional ways.
The economic distress people suffered also helped his cause. Because the Versailles Treaty severely restricted the size of the German army, many ambitious young men found themselves with that career path cut off. Prior to war, a young man with no wealth could find a respectable career in the military. Now, these unemployed men had almost no opportunities and were ripe pickings for the Nazi brownshirts whom Hitler's friend Röhm organized. Further, as the Depression hit, people wanted better leadership—not a government that sat on its hands—as well as food and jobs. Hitler promised all this.
Hitler's location in Munich was helpful for recruiting, and he also pounded home the idea that Germany, shrunken after World War I, needed land to grow and feed its people. British blockades and lack of German government planning had lead to starvation during World War I, so Hitler's expansionist politics found a receptive audience.
Finally, many people in Germany rejected the democratic socialism of the Weimar Republic. Hitler's ideology, which strongly rejected democracy and equality as weakening the German Volk, appealed to many. People were used to a kaiser or strong leader(s) with a great deal of power ruling the country or pieces of it (Germany didn't unify until 1870). Hitler rejected modern concepts, such as female equality, that troubled many people, and he looked back nostalgically to a better world that had never existed but which he could conjure as an alternative to the problems of modernity.
Hitler also had a flair for propaganda, designing the easily recognizable and striking Nazi flag, while using newspaper technology, including photography, to send out a constant barrage of propaganda. As he gained power, he used airplanes for travel, allowing him to quickly cover long distances. Arriving by plane also gave people the impression he was descending from the skies like a god or savior to Germany.
Hitler exploited a perfect storm of economic distress, German humiliation that found a scapegoat in the Jews, the desire for a Messianic leader, and a yearning for tradition that catapulted him to power.