Something I can answer!
Short answer: The Wall Street crash and Hitler's oratory skills
Long answer: To understand how the NSDAP (The Nazi Party) got it's sudden burst of popularity (800,00 to 3,000,000 in 4 years. That's the same as approximately 5 new voters every minute of every day for the next 4 years) you first need to know about the Dawes Plan. The Dawes plan was a series of agreements with the US and Germany after the first world war involving mainly huge reperation loans of over 3 billion German marks (currency) over 5 years. This was taken in two very different ways by both sides of the Weimar Republic (the government in Germany at the time after WWI) the left wing were very positive of the arrangement, believing that as long as they behave and accept all foreign aid then they will be forgiven for their crimes in WWI. The right wing however believed that it was a bad idea and that relying purely on another nation's wealth was un-German and demeaning. Unfortunately, after the Wall St. Crash the right wing were proven correct when the US suddenly called back it's loan and Germany was left in massive debt.
As this was occuring Hitler was busy rallying support as an anti-semitic and nationalist leader, giving huge speeches and writing manifesto's that were met with amazingly positive reactions, people were said to have even been chanting "Sieg Heil!" after his speeches despite Hitler's rise to totalitarian power not occuring for another half-decade. You must also understand that during this time the majority of German people were anti-semitic and xenophobic, hating foreign nations even more after the collapse of their economy.
Fears of Jews from the East and a lingering hatred for other nations left over from WWI gave Hitler a perfect foot-hold into government and, despite the NSDAP being a fairly small and new party allowed them in 1932 to get a majority vote in parliament and in 1933 Hitler was appointed chancellor of Germany.
I hope this helped you. If you have any other questions field them to me in the replies.