The best way to do this is to read through the story, and try to shrink each paragraph down into one or two simplified sentences that summarize the main point of each. I'll give a brief summary below, along with links that will lead you to the story itself so that you can do a more detailed summary; space doesn't allow it here.
There is a man who becomes obsessed with an old man in his building with one bad eye that is filmed over. He compares the eye to a vulture (a symbol of impending death and watchfulness) and learns to hate the eye so much that he ends up wanting to murder the old man. He goes to the old man's room at night, opens the door a bit until his lantern can see the old man, and just watches him. One night the old man awakes in the darkness, and the narrator goes in very stealthily and kills him. He buries him under the floorboards in his dwelling. The police come and start questioning him about the old man; the narrator is so confident in not getting caugh that he asks them in and sits down right on top of where the man is buried. But then he hears what he feels is the old man's heart beating beneath the floorboards. The beating gets louder and louder; the narrator is certain that the police can hear it! He finally, when the beating is so loud he can stand it no longer, confesses. The beating heart noise is a symbol of his own conscience for having murdered the man.