The 'final solution' was a euphemistic phrase that referred to the extermination of all the Jews in Europe. German leaders had become impatient with the process of conventional execution. In short, they felt that these methods did not kill a large enough number of Jews at any one time.
The Nazi leadership then gave orders for the setting up of extermination or death camps. The first was at Chelmno, with subsequent camps in Sobibor, Belzec, Treblinka, Majdanek, and the infamous Auschwitz-Birkenau. Deportation orders were often given around the Jewish holidays, and Jews were always rounded up near train stations. Those who did not or could not keep up the pace were quickly shot.
Once at the camps, some were separated for forced labor, and others were sent straight to the gas chambers. The weak, old, and infirm were immediately dispatched to their deaths after the order to disrobe completely. The stronger Jews were often made Sonderkommandos. Their job was to separate and catalogue any valuable Jewish belongings for Nazi appropriation and to transport the dead bodies of their countrymen to the crematoria (these were just large pits where bodies were thrown in and burned). Many Sonderkommandos were eventually murdered after some months of this cruel work. They were replaced by fellow Jews before they too, went to the gas chambers.
Hundreds were being gassed by the hour in gas chambers. In Auschwitz, at the height of operations, soldiers were sending almost 6000 people to their deaths each day. The more packed a chamber was, the faster the people suffocated to death. Gas from huge tanks were piped into sealed chambers; in due time, faster-acting poisons were used such as Zyklon B. Zyklon B pellets immediately converted to lethal gas upon contact with air.
The Nazis left nothing to chance. Their methodical killing methods were effective, merciless, and final. Thousands died every day in sealed chambers, while Jewish slaves worked to dispose of dead bodies. All the leadership had to do was to make sure these death operations continued with cold-blooded precision until all the Jews and various marginalized groups were exterminated.