There are examples of each of these in "The Most Dangerous Game," but the fact that you need help suggests that you are not familiar with these literary terms, so before I offer each example, I will explain each term.
First let's talk about personification. That is a way of suggesting that an object or an animal is a person, or is doing something that a person would do. For example, if I were to say, "The sun smiled down on me," I would be suggesting that the sun can smile like a person, which of course it can not! In the example below from the story, the writer is suggesting that the night is a person who could press himself against the yacht.
Can't see it," remarked Rainsford, trying to peer through the dank tropical night that was palpable as it pressed its thick warm blackness in upon the yacht.
Now, a simile is simply a statement that describe something in terms of something else. For example, I might say, "This cloth is lke sandpaper," indicating it is very rough or coarse. What follows is a description of the night, comparing it to velvet.
"Nor four yards," admitted Rainsford. "Ugh! It's like moist black velvet."
Finally, a metaphor is a statement that describes something in terms of something else, much like a simile, but instead of saying,"This is like that," a metaphor says, "This is that." An example might be my saying of someone I love, "He is my sunshine." Actually, there is a song entitled, "You Are the Sunshine of My Life," now that I think about it. The example from the story shows a metaphor that tells the reader that Rainsford is being hunted and that the General is hunting him, just as a cat will hunt for a mouse.
The Cossack was the cat; he was the mouse.
This is a story that is filled with many examples of personification, simile, and metaphor. See if you can find some, too.
You can see an example of simile just about as soon as the story begins. Simile is when you compare two things using the word "like" or "as." Cornell does this when he has Rainsford describe the weather as "Ugh! It's like moist black velvet."
Personification happens a little farther down when Cornell personifies evil. He says that it "can, so to speak, broadcast vibrations of evil." Of course evil can not really do this -- it is not animate and cannot broadcast anything. Later on still, the sea has "greedy lips" that it licks.
Finally, after Rainsford has met Zaroff and gone to bed for the night, he couldn't "quiet his brain with the opiate of sleep." Here, the author is calling sleep a drug -- comparing the two but not explicitly like a simile does.