I'm reading Maus, and mentioned frequently are the true rumors about the camps and the gassing that reached the outside. How did this information make it out?
It was by a large part due to the efforts of the Polish resistance. Polish prisoners of Auschwitz, especially those affiliated with the Armija Krajow (the home army) and the Internationale Kampfgruppe Auschwitz (international combat group) collected evidence in the camps, which they smuggled outside.
The first of these reports (mostly written by camp resistance leader Witold Pilecki were brought out of the camps by escapees in 1942. They were quickly picked up by socialist and Polish nationalist underground newspapers as well as by the Polish government in exile in London.
This happened quite frequently (with the most famous one probably being the Vrba-Wetzler report in 1944) and so knowledge of the Holocaust spread as rumors in Nazi occupied Europe and press reports in the Western world.
Another source of information was the Soviet Press and Propaganda. Although often assumed and perceived to be atrocity propaganda, the USSR started very early to collect evidence of mass shooting and deportation.
This all made it into propaganda broadcasts and of course the world started to spread.
Sources:
Raul Hilberg: The destruction of the European Jews, Yale 2003.
Szabó, Zoltán Tibori (2011). "The Auschwitz Reports: Who Got Them, and When?" in Randolph L. Braham and William vanden Heuvel: The Auschwitz Reports and the Holocaust in Hungary.
Well, for starters there were a number of people who were able to successfully escape not only the ghettos, but the camps themselves. We have first hand accounts of people who got out. In Sobibor, there was a mass escape as well of nearly 300 inmates. Many were re-captured, but about 50 survived to the end of the war.
I have a friend who escaped from a ghetto, and whose life story I know quite well. He says that there were indeed all types of rumors floating around, but most of the people in his town didn't believe them. Luckily for him, his mother did!
http://www.amazon.com/What-On-Earth-Doing-Here-ebook/dp/B003Z9K5N0
Here's his autobiography; it's a fast and exciting read if you're interested.