1924-29 was what Hitler called the lean years. Stresemann had signed the Dawes plan in 1924 reducing annual payments and ensuring American bankers invested in German industury (take note of this). Stresemann then managed to lower reparations to £2 billion in 1929 but stretching them out until 1988 and even managed to join the League of Nations in 1925 - a sign of international approval. All of this restored German faith in the Weimar Republic. This is why the Nazi party only got 12 seats in the 1928 election - 20 less than 1924.
Hitler reorganises the party around this era. He worked with Dr. Joesph Goebbels to create propaganda, created clear scapegoats to blame issues on i.e. Jews, showed Hitler as the party's voice and used the SA to show power and sophistication. He also creates the SS as the new bodyguard service since the SA begin to develop loyalty to Ernst Rohm, the leader.
Then Hitler got lucky. The Wall Street crash in 1929 hit American bankers hard which as you remember, support German industry. This leads to unemployment and business failure. And guess who was to blame according to Hitler? The Jewish bankers.
The current chancellor (Bruning) was extremely controversial and raised taxes to support poor people financially. Good idea when everyone is affected just as badly since this affects both workers and businessmen. He also bans demonstrations but obviously this is removing the right to free speech (according to Nazi propaganda). Re-elections are called due to the unrest.
The Nazis gained more seats this time - 107. People saw him as a strong figurehead who could reunite Germany and scrap the Treaty of Versailles - the diktat. They saw the SA as a powerful force which are owned by the Nazis which shows strong leadership skills. A few SA troops were probably positioned around poll booths also.
The other key point is that it promises hope for everyone. The workers get a promise of work and bread and conservative German values. These also attract the middle class who believed Hitler could restore prosperity and want traditional German values.
National socialism involves placing private land under government control. However, Hitler says that land will "only be taken of Jews" attracting the farmers and businessmen. They saw it as a lesser of two evils when comparing it to communism.
Young women also saw Nazism as the best way for their family through propaganda. Some were attracted to his passionate speeches and his high ambition.
In 1932, The Nazis were the biggest Reichstag party (but not a majority). Hitler ran for president but Hindenburg (the current president) managed to retain his presidency. The not-so-popular Bruning was sacked and von Schleicher took control. He put von Papen forward as a chancellor (he preferred to control behind the scenes) and allowed the Nazis to join the coalition government. Then in the July 1932 elections, Hitler had increased his seats to 230 and declared that von Papen should get sacked.
Von Papen called for an election in November 1932. Hitler's number of seats fell, but it was still the largest party. Hindenburg instead appointed von Schleicher as a chancellor. He then threatened to form a military dictatorship making hin so popular that he lost all support in the Reichstag.
With nobody else to go to, Hindenburg declared Hitler as chancellor in January 1933.