To whom is Montresor telling the story in "The Cask of the Amontillado" and how do you know this?

This is a good question because it is not immediately nor obviously clear who Montresor is talking to. Note the second line of the story. Montresor says, "You who know so well the nature of my soul . . ." This is a pretty suggestive statement. We might think he is talking to a trusted friend or a spouse, an intimate friend, or someone he trusts. 

At the end of the story, Montresor reveals that...

This is a good question because it is not immediately nor obviously clear who Montresor is talking to. Note the second line of the story. Montresor says, "You who know so well the nature of my soul . . ." This is a pretty suggestive statement. We might think he is talking to a trusted friend or a spouse, an intimate friend, or someone he trusts. 

At the end of the story, Montresor reveals that it has been 50 years since he's killed Fortunato. So, he's clearly much older. One might question why he decides to confess his sin to someone so long after it has occurred. There are a lot of religious undertones in the story/confession. Montresor gives his warped version of the Golden Rule in the beginning of the story. "A wrong is unredressed when retribution overtakes its redresser." There is the notion that Fortunato's consumption of wine is his "last supper." Montresor concludes the story/confession with "rest in peace" (In pace requiescat). So, even though he doesn't seem very contrite or remorseful, this seems to be a confession to a priest. Montresor is fifty years older and therefore quite old at this point, maybe close to death. Therefore, he might finally feel inclined to confess. A priest who would know Montresor's sins would know the "nature" of his "soul" as a result.