At home, while playing games.
It was on reddit all the time, so after seeing a few clips and enjoying them, and seeing that he got some decent guests on there, I started watching them as they came out. In May 2012 I stopped watching it regularly, but missed sitting with Minecraft or GTA open, listening to America's politics being eviscerated. At some point, in 2012 I guess, I started watching them again, and certainly by February 2014 I was watching more or less every episode.
On the 8th of August 2015 I watched the final episode with Jon Stewart. Many of the 'correspondents' had come and gone in the time I'd been watching it, and finally it was time for the host to move on.
I wonder if it will continue to be interesting to watch. I shall certainly find out.
Update Jan 4th 2016: I've watched a couple of episodes with Trevor Noah but I don't ever get the urge to watch it. It's not the same.