The narrator didn't like the old man's eye. He watched him sleep at night every day for a whole week so he can try and kill him.
On the eighth night, the narrator was very cautious about opening the door and sneaking in. It was very dark in his room when he accidentally lost his grip on the handle of the lamp and it fell down hitting the lamp and the old man saying "Who's there?"
The narrator grabbed the old man's bed and put him underneath; squishing him to death.
The narrator then cut him up in a bathtub and put him under the floorboards where you wouldn't even notice he was there.
The next morning, police showed up at the narrator's door and started asking him some questions. The narrator got more nervous the more time the police spent at his house. Then the narrator got so nervous he told where the old man lied.