How were the murders during the Holocaust accomplished?

Jews and others were rounded up, many on Krystalnacht which was the beginning of the Holocaust. They were put into cattle cars, the claim was that they were being moved out until the end of the war or that the German government needed their resources. The cattle cars stopped at concentration camps where the people were told that they would be living in the dorm's until the end of the war or until they could be relocated. Groups of Jews and anyone else that the Germans hated, were told that they were being sent to a disinfecting chamber, which actually turned out to be a gas chamber. The doors were locked and gas was pumped in. Sometimes they were just marched into a field and shot. The Germans were efficient and were given instructions to find the cheapest way to kill the Jews... and they did it, over 2,000,000 times.