Modern media does not do them justice, but Hitlers speeches were notoriously exceptional, public speaking was his main, great skill. This goes back to 1919 when Karl Mayr picked him out whilst giving lectures to ‘nationalise the army’, (prior to joining the DAP) and he was renowned from his very early days speaking in the Munich beer halls, right up to the big rallies, that held hundreds of thousands of people. There were even instances of people convulsing and deficating in excitement at his rallies! Think like a political version of a televangelist.
However, why people voted NSDP was a different issue. It is a somewhat complicated issue, that is still researched and debated, but I will try to summarise what I see as a few key points.
In spite of how good he was at speaking, he was not a ‘pied piper’ who put people under his spell and magically got them to vote for him - they had their reasons, that Hitler and the Nazis brilliantly exploited. However, that is not to say that the figure, and ‘charisma’ (in the Webian sense) of Hitler was not absolutely paramount to the regimes popularity, as Kershaws ‘The Hitler Myth’ has shown.
A key factor in the rise of the popularity of the NSDSP was the Great Depression. In 1928 the NSDSP received 2.6% of the vote in the Reichstag elections of that year - this increased to 37% in 1932! The Depression took a huge tole on a Germany, already ravaged by the hyper inflation of 1923, not to mention the war, and near civil war (with the extensive political chaos of the early 20’s). People, who had faced unemployment and economic ruin, were not only desperate for anything that could get them out of the mess, but they had lost all confidence in the status quo and conventional political parties in order to do so. So, whereas all the other parties (except the communist KPD, who were the only other party rise in popularity in this period) represented a resumption of the - perceivably failed - status quo, the NSDP offered something innovative, new, fresh, and untarnished by the perceived failures of the Weimar Republic.
In addition, the NSDAP was able to organise brilliantly (especially with the input of Gregor Strasser), and appeal to a wide range of the electorate, and therefore siphon votes from the more traditional parties - from socialists to conservatives - was absolutely key. Not to mention fully exploring the figure of Hitler, and his speaking, as the leader who could lead Germany not only out of the depression, but towards a national redemption, which could be seen as very appealing to a hitherto proud nation, that had experiences enormous political and economic strife.
They also managed to portray themselves as the party of law and order, and of national unity - ‘ein volk, ein reich, ein Fuhrer! Germany (a relatively new nation, politically speaking) was divided politically, something that was exacerbated considerably by the depression and chaos of the early 20’s. The Nazis however offered unity, and end to division and infighting, that all Germans were part of the ‘peoples community’ (volksgemeinschaft), which again was extremely appealing. Furthermore they stepped up violence against the communists on the streets, portraying them as an enemy of the German people (fully exploiting the terror in the Russian civil war of the early 20’s), so any violence against the communists was portrayed as the Nazis protecting the German people, as a necessary step in state security (this would also be used later to justify the ‘Reichstag Fire Decree’, and camps like Dachau for alleged political enemies).
What people did not vote for was antisemitism, racism, eugenics, war and extermination camps. During the early 1930’s, Nazi propaganda and political agitation about Jews was toned down considerably, as they knew it would be seen as being too extreme for all but the most right wing ideologue of the party.
In order to appeal to the masses, they again focused on the economy, denigrating other political parties, and protecting Germany from socialism and socialist revolution. It is worth remembering though, that although Hitler did not hypnotise people through his speaking, his figure, and the mythos that was quickly developing around his character (call, by Joseph Goebbles, his ‘greatest achievement’), was still a key element in appealing to the electorate, and as a means of addressing their dire needs.
Some books you may find useful are, Kershaw, I The Hitler Myth, and Rees, L The Dark Charisma of Adolf Hitler.