During the exposition of The Tell-Tale Heart we are introduced to our protagonist. We do not know his name. All we know is that the story takes place in the old man's house, the story takes place primarily at night, and that it is cold. We learn that the narrator wishes to kill the old man because of his eye, his eye being the antagonist. The narrator talks of the old man very greatly but his eye makes our protagonist feel strange.
We learn that the narrator has a plan to kill the old man. He opens the door very slowly, slower than the minute hand on a clock, and then he peaks his head and a lantern out at the same speed. He then watches the old man sleep. We are informed that for seven nights the narrator has been watching the old man sleep, but cannot go through with killing him because he can't see his eye.
On the eighth night the narrator follows through with his plan because of how he accidentally made some noise and woke him. By waking him he was able to see the pale blue eye that made him wish to kill him in the first place. In this scene you can see the narrator jumping towards the old man just before he ends up killing him. After he kills him he cuts up his body and hides the pieces under the floor boards in this room.
During this part of the story the police show up to the house because a neighbor called the police and said that they heard a shriek during the night. The narrator is very calm and talks to the police with ease and confidence, but then he starts to hear a heartbeat and gets nervous that they can hear it as well.
In the resolution of the story the narrator turns himself in. He only does this because he believes that the police officers can also hear the heartbeat from the floorboards. Once he thought this he started to get more and more nervous until he finally cracked. When he did crack he told the police how the body is hidden under the floor boards.
The conflict of the story is external, being the narrator versus the eye. And the theme of the story is that eventually the truth will reveal itself, this theme is in the story from how the truth that he killed the old man revealed itself because it made the narrator cracked.