Hitler started to rule Germany because he was appointed chancellor. In the German political system of the time, there was a President who was the head of state. That person had the right to appoint a chancellor. The chancellor was essentially equivalent to a prime minister in countries like the United Kingdom.
Chancellors could essentially be picked by election, but that is not how it happened with Hitler. In his case, the elections were inconclusive and no party could gain a majority. Eventually, political leaders convinced the president, Paul von Hindenburg, to appoint Hitler as chancellor. The Nazi Party had been relatively strong in the elections and the political leaders felt that appointing Hitler would gain their support. They felt that they, the leaders, could manipulate Hitler. Obviously, they were wrong.
Once in office, Hitler used the organization of the Nazi Party to destroy his opponents. He used political violence and threats of violence to take more and more power to himself. Soon, he essentially had absolute political power in Germany.
Thus, Hitler started to rule Germany by being appointed to office and then by using that office and his Nazi Party organization to take complete control of the country.
He saw that the depression in Germany as a way to rise in power, so he did many good things to help Germany, resulting in the Nazi party and war.