Desperation + Well-Spokeness, Charisma, and a little bit of a palatable ideology.

The Treaty of Versailles left the German Republic shrunken down, demilitarized, and nationally humiliated.

The Weimar Republic's currency was worth close to nothing due to the great depression, a loaf of bread could cost about as much as a sports-car.

The country had close to no law and order and was led by a terribly inefficient gov't, back-alley surgery, mother-daughter prostitute teams, homeless veterans, instances of public masturbation at Cabarets, and street-fighting between political militias were standard-fare. Political divisions were very bad, Nationalists who yearned for the day of the capitalistic, militarily-impressive German empire clashed with the Communists who wanted Weimar to become little more than a Soviet satellite state, many of the latter having begun to view their circumstances as "capitalism in decay".

Close to no Germans were happy with the state of things, everyone wanted it to be replaced by a communist state or a third reich...of some variety.

Nazism was an ideological compromise, Socialism and Anti-Capitalism for the Left, Nationalism, Militarism, and Anti-Communism for the right.