In general, the Final Solution evolved from an unorganized, generally anti-Semitic set of tendencies to a very organized program of genocide.
At first, there was no real thought put towards systematically exterminating Jews. The Nazis were content to let them leave the country (especially if they left their property behind).
The move towards a Final Solution started after the war began. At first, the killing of Jews was conducted mostly against Jewish populations in Eastern Europe. These were conducted by Army groups called Einsatzgruppen. But these killings (by shooting) were inefficient and too stressful on many of the soldiers. From there, the Nazis "innovated" new ways to kill Jews in massive numbers and the extermination camps were created.
The Final Solution initially started with the dehumanization of the Jews, who were increasingly classified in German society as humans with no rights – they thus had to be demarcated as separate with identifying marks. This was followed by ghettoization as Jewish citizens were forcibly moved to older and poorer neighborhoods and literally fenced in or confined there by the German police, as well as the military.
Such policies were stepped up with the launching of Operation Barbarossa – the war was to be treated as a war of imperial encroachment. The Nazi state drew a heavy and close relationship between their aims of destroying the communist state and obliterating the Jews, who formed the principal targets. Orders were issued via the army in March, April and May 1941 and mobile killing was carried out by the Einsatzgruppen, which were heavily armed mobile killing squads that were used to eliminate all the undesirables in German-occupied territories.
However, there were simply too many of them to be killed. The tactic of using the Einsatzgruppen was failing since there were too many race enemies for the squads to deal with. It was extremely inefficient to continually increase the number of Einsatzgruppen to be used as that would only strain Germany’s military capability.
It was impossible to physically transport all the Jews out of Germany, since that meant a possible massive outburst of Jewish refugees to the rest of Europe and most nations on the continent proved unwilling themselves to take in such large numbers of Jews. Perhaps in this manner, the other European states could be considered to have been complicit in the Final Solution – they did not provide a haven for the persecuted Jews for fear of a possible backlash. However, in reality, there was simply not enough shipping to have moved all the surviving Jews out of Central Europe; no one in Europe had also expected the Nazi state to undertake such an extreme policy of mass extermination. As a result, the Germans had to turn to mass extermination and industrial killing through the establishment of death camps to get rid of the Jews since there were no other options available. The policy they adopted grew very naturally out of what they had already been doing and did not divert significantly from the Nazi worldview.