The Narrator is explaining to us that he is not crazy. And also killed an old man because of his creepy eye.
First the Narrator is being nice to the old man to make the old man less suspicious of the evil deeds soon to befall him.
The Narrator now practices sticking in the lantern and his head through the door to watch the old man.
It's time for the old man to die, but the one night the Narrator was ready to kill the old man, he was awake!
The Narrator braved the watchful gaze of the evil eye and pranced on top of the old man, wrestling him to the ground finally suffocating him under his own mattress.
Unbeknownst the Narrator a neighbor had heard the screams of the old man and contacted the police who sent over two officers to check out the noise. The Narrator tried to play cool but he turned himself in after hearing the "old man's heart."