How was hitler's "final solution" carried out by the nazi regime?

 Millions of Jews, along with other unwanteds, were exterminated in mass killings.  The Nazis used firing squads and poison gas as a means of killing in their extermination camps.  They also sought to kill all Jews in the Jewish settlement region of the Soviet Union as German forces went through that territory when invading the USSR.

Further context:

The Holocaust was the mass extermination of Jews and other unwanteds in Germany during World War II.  The Nazi Party under Adolph Hitler was in charge in Germany at the time.  This was a fascist and nationalistic form of government.

Hitler and the Nazis believed in the supremacy of what they referred to as the "Aryan race" -- which was a term they used for the Germanic peoples.  They believed their race was superior to "lesser races" like the Jews, blacks and others.  Hitler and the Nazis mounted a campaign in Germany to promote their race over others like Jews and Roma (gypsies), etc.  

They enacted what are called the Nuremberg Laws, which were passed at a Nazi rally in Nuremberg in 1935.  These laws denied citizenship and other rights to Jewish persons.  The Nazi campaign against Jews got even worse from there.  They rounded up Jews and put them in concentration camps (which later became extermination camps).  In support of their World War effort, they used Jews for forced labor in the concentration camps.  They also used Jewish persons and others they deemed undesirable essentially as laboratory rats for doing unethical medical experiments on them. For example, they'd put persons in a pressure chamber to find out how high an altitude they could let their pilots fly before they'd become unconscious from the altitude and pressure.  Others of their experiments were even more gruesome.  

Ultimately, there was what the Nazis called "The Final Solution" (in the 1940s), which was mass extermination of the Jews.

d.)   when the us left nato after the end of the cold war and they had to evolve to focus on more humanitarian measures with the smaller budget