Take a story's temperature by studying its tone. Is it hopeful? Cynical? Snarky? Playful?
Casual, Curmudgeonly
To make the whole "this is the diary of a madman" idea believable, Gogol really had to nail this one, and we think he did. The way Poprishchin describes everything is so casual and matter-of-fact that it's not that hard to take his word that he thinks this is all really happening.
Look at this guy—he has just heard a dog talk and he's acting all cool: "I confess, I was very surprised to hear her speak in human language. But later, when I'd thought it over properly, I at once ceased to be surprised" (2.1). Or he has just pushed his way into a stranger's apartment (a single woman's, on top of it), taken some papers from her dog's basket, and gotten bitten by the dog. What does he say? "I suppose the girl took me for a madman, because she was extremely frightened" (7.1). Gogol makes him say all this in such a matter-of-fact way that it becomes easier for us to go along with it. On the other hand, the fact that he can talk about all this stuff in such a casual and detached way, even when he logically "discovers" he's the King of Spain, just emphasizes how out of touch with reality he is.
Poprishchin's tone is also really curmudgeonly: he says horrible things about everyone: the Jews (1.1), the provincial government (1.1), the French (2.1), women (7.1), the Finns (7.1), Muslims (13.1), the English (18.1)... it's a long list. He's full of suspicions and thinks the worst of everybody.