What are the first events in Edgar Allan Poe's "The Black Cat"?

Technically speaking, in Poe's story "The Black Cat" the first thing that 'happens' is that the narrator informs us he is going to die tomorrow and wishes to unburden his soul tonight by exposing "a series of household events" that have terrified, tortured, and destroyed him in the time leading to this moment. 

You asked which events happen first, but I am not sure how far into the narrative you would like to consider as "first events". The sequence of events he describes are as follows:

1. The narrator had a normal childhood and was known to be docile and fond of animals.

2. As a young man, he married a woman who also loved animals and brought a lot of pets into their household.

3. The narrator developed a fond relationship with their black cat named Pluto.

4. The narrator began to drink excessively, which resulted in violent tendencies.

5. One day while drunk, the narrator cut out Pluto's eye with a penknife.

6. Pluto thereafter began to avoid the narrator, which caused the narrator to feel perversely annoyed by Pluto.

7. The narrator placed a noose on Pluto's neck and hung him from a tree in the garden.

8. On the night of the hanging, the narrator's house caught fire, and everything was destroyed except for one wall in the middle.

9. The narrator thought he saw the figure of a cat on the remaining wall and then tried to think of a logical reason how the shape could have been put there.

10. After months of obsessing about the incident, the narrator noticed a different black cat at the "den of more than infamy" where he was drinking, and led the cat home with him.

11. The narrator began to hate the cat, while the cat began to like the narrator even more.

12. The narrator thought the cat's white spot suddenly seemed disturbingly shaped like the gallows.

13. The cat followed the narrator and his wife into the cellar one day. The narrator attempted to kill the cat with an axe, but his wife grabbed his arm, so he plunged the axe into her head instead.

14. The narrator decided to wall his wife's body up in a wall of the cellar. 

15. After three days of not seeing the cat anywhere, the narrator felt relieved he would no longer have to look at it.

16. On the fourth day after the murder, police came to investigate the premises.

17. The narrator bragged to the police about the solid construction of his house and rapped on a wall with his cane to prove how strong its walls were.

18. The rap on the wall was answered by a voice from within the wall.

19. The police tore the wall down and found the corpse there with the cat perched on its head.

We can assume the narrator was probably then arrested, tried, and sentenced to the death penalty, as the beginning of the story appears to be a confession on the eve of a death he knows is coming the next day. A death sentence seems more likely than that he simply lived a long life and feels like he will die of natural causes tomorrow. Being sentenced to death is also more likely than the narrator planning to kill himself out of remorse because he seems to blame the cat rather than himself for his actions.

In "The Black Cat" by Edgar Allan Poe, what is the inciting incident?

The inciting incident in a story is the event that takes place that causes the protagonist to take action or "get things going."  Without the inciting incident, the story would not take place; there would be no action.  The inciting incident is where the action of the story begins, and it should grab the reader's attention. This is the event that must happen in order for everything else to happen, so it should take place near the beginning of the story.

In Edgar Allan Poe's short story "The Black Cat," the reader is given a considerable amount of background information in the exposition of the story.  Then comes the inciting incident.  It takes place when the narrator recounts the events of an evening when he came home drunk and encountered Pluto, his favorite pet.

One night, returning home, much intoxicated, from one of my hauints about town, I fancied that the cat avoided my presence.  I seized him; whe, in his fright at my violence, he inflicted a slight wound upon my hand with his teeth.  The fury of a demon instantly possessed me...I took from my waistcoat-pocket a penknife, opened it, grasped the poor beast by the throat, and deliberately cut one of its eyes from the socket!

Had the narrator and protagonist not come home inebriated and cut out the cat's eye, he would not have become obsessed with the cat's behavior or murdered his wife when the she interfered in his attempt to hit the cat with his axe.  The plot would not have taken place.

How does the story "The Black Cat" by Edgar Allan Poe begin?

Poe's opening paragraph of this first person narrative raises the reader's curiosity and leads to the expectation of a bizarre story. The narrator invites the reader to construct his or her own meaning from the tale he is about to tell, saying that he doesn't expect to be believed. He states as well that to some readers the story may seem less horrible than it does to the narrator. He speculates that some will find the story baroque, by which he means complicated, rather than "terrible." He even says that a mind calmer and more logical than his own may construct a perfectly ordinary meaning out of his tale, one that does not rely on the supernatural.

As is typical with a Poe story, the narrator insists he is not mad, which, of course, leads us to believe that he has been accused of insanity and perhaps may indeed be insane. We find ourselves primarily teased to read onward by this opening, wondering why the narrator says he will die tomorrow and what "series of mere household events" is causing him to react with such drama. Poe shows here, as in other stories, that he is a master at pulling the reader into a tale.