In "By the Waters of Babylon," how do you know the narrator is dreaming when he falls asleep in front of the fireplace?

Well, we are not told specifically it was a dream. It
could have been a very strong vision. Either way, it is clear that somehow John, the
narrator who tells us this story, is seeing the city as it once was rather than seeing
its reality in his time. He describes to us a strange sense of being drawn out of
himself into the past to witness what he then goes on to narrate. Consider the following
description:

I
know that I felt myself drawn as a fish is drawn on a line. I had stepped out of my
body--I could see my body asleep in front of the cold fire, but it was nto I. I was
drawn to look out upon the city of the
gods.

It is clear that the
city he sees is transformed greatly compared to the ruins that he has just made his way
to. He sees lots of light and hears roaring sounds, which we can obviously relate to the
lights at night and the sounds of a city in our time. Thus it is that John does
experience some kind of powerful vision, when he witnesses how the Gods were destroyed,
but it is suggested that this is not a dream.