Short answers, pulled from the story.
The six Nazi extermination camps were Auschwitz-Birkenau, Treblinka, Bełżec, Chełmno, Sobibór, and Majdanek. All six are located in present-day Poland, placed near branch rail lines connected to the Polish railway network for the mass deportation of victims.
According to the United States Holocaust Memorial Museum, an estimated 2.7 million people were murdered across the six extermination camps. Auschwitz-Birkenau had the highest death toll, with an estimated 1,100,000 killed between May 1940 and January 1945.
The primary method was gassing. The Reinhard camps (Treblinka, Bełżec, and Sobibór) used carbon monoxide produced by internal combustion engines. Auschwitz-Birkenau and Majdanek used Zyklon B, a cyanide-based product manufactured by IG Farben. Chełmno used carbon monoxide vans.
Extermination camps were built exclusively for mass killing, with deportees at Bełżec, Sobibór, and Treblinka typically murdered within hours of arrival. Concentration camps, such as Dachau, Buchenwald, and Mauthausen, were prison camps set up for people the Nazis deemed undesirable, where prisoners were held for slave labour rather than immediate killing.
Chełmno was the first to begin operations, in December 1941. Bełżec opened in March 1942, Sobibór in May 1942, and Treblinka in July 1942. Auschwitz was fitted with new gas chambers in March 1942, and Majdanek had them built in September 1942.
The Nazis disguised the killing programme through the secretive Sonderaktion 1005, which involved exhuming and incinerating bodies originally buried in mass graves, destroying records, and dismantling the camps using condemned prisoner labour. Internal communications referred to mass murder only by euphemisms such as "special treatment" and "resettlement".