Well the Nazis first wanted to rid Germany of Jews, since there were certain Jews who were very wealthy, so they installed a fee for Jews that wanted to leave the country. With that they got rid of them but their money stayed in the country. The fee was 25% of the persons or families funds and was raised from year to year. Wich means poor Jews couldn't leave Germany. After the "Reichspogromnacht" 1938 more and more Jews began to flee and after the start of WW2 in September 1939 the last big wave of Jews fled the Reich. Until 1941 Jews were already being killed e.g. in shootings or similar methods, so nothing with a specific system behind it. After the Nazis knew the war is going to be lost since they couldn't push any further against the Soviets, thee thought to themselves "now we gotta kill them". At the "Wannseekonferenz" 1942 they discussed the current situation on the Jews and developed ways to kill the most "efficient" and they got to the gas "Zyklon B". After Wannsee the first concentration camps were build and the systematic and planned killing of the Jews began in order to "cleanse" Europe of the Jews. This intention is referred to as "Die Endlösung der Judenfrage" or the final solution of the Jewish question.