In "The Tell-Tale Heart" by Edgar Allan Poe, how does the narrator eventually murder the old man?

This question can be answered through a close reading of the text; in it, the narrator describes his struggle as he murders the old man, and what he does with the body afterwards.  I encourage you to take a close look at it and read it for yourself, because it's such a cool story, and the way that Poe writes it is super intense.

To summarize, the narrator opens the door to the room and eventually, shines the lantern onto the old man.  And, it is the old man's creepy eye that falls into the beam of the lantern.  This, along with his perception that he can hear the old man's heartbeat, makes the narrator so incensed that he attacks the old guy.  Poe describes it thus:

"In an instant I dragged him to the floor, and pulled the heavy bed over him."

So, he basically smothers the old man with the mattress.  The narrator mentions how it took quite some time for the old man to be smothered to death, and for his heartbeat to stop beating away.  But, after the deed was done, the narrator takes gruesome means to cover the crime--he chops the old man's body to pieces in the bathtub, and buries the parts under the floorboards of the room he was murdered in.  Pretty horrific, if you ask me, which is probably one of the reasons that for nearly 200 years, this tale has been so popular.  Poe has a talent for writing really interesting narrators who do some pretty fantastical things.   I hope that helped; good luck!