If you want to be very detailed in this answer, as you read you should search for examples of figurative language (similes and metaphors). Rowling uses several in all the Harry Potter books.
On a broader scale, however, the most noteworthy literary elements for analysis in any of the Harry Potter books are going to be things like point-of-view, setting(s), symbolism (in objects, characters, and the many symbols--used as labels--found throughout Hogwarts), and foreshadowing.
Symbolism is probably the largest and easiest element to look at. This book is the first in what becomes an entire series of fantasy books that encorporate very unique story lines with very traditional elements of good vs. evil, magic, mystery, and fantasy. Everything in Harry's world is symbolic of something else. Consider for example, the four houses at Hogwarts, the symbols associated with each, and the traditional associations that come with each. Consider the difference in symbols used for good vs. evil and the way each character is associated with either an animal, natural element, or some other identifying object that gives insight into his or her personality.
Additionally, you could analyze the above techniques through one of the main themes of the book. Finally, because the story is written at about a 5th grade level, you could look at the elements of foreshadowing throughout the story as the mystery (and Harry's historical back-story) are slowly revealed.