First you'll need to decide on a meaningful theme. I might suggest using the disillusionment of the American dream as the basis for your analysis. It would be feasible to construct a thesis arguing that Fitzgerald's ultimate purpose is to demonstrate that the American dream is an illusion and that efforts to fully realize it lead to destruction.
You could construct body paragraphs that then examine how each of the following contribute to this overall theme:
- Nick's narration: Imagine what a different novel this would have been if Gatsby had narrated the story. The mystery behind the central character would be lost, and the intrigue inherent in Gatsby's character would be diminished. Using Nick as a narrator allows readers to get to know Gatsby by degrees, the details of his past and his business dealings emerging slowly over time. In this way, Nick's narration allows Gatsby to be somewhat of an illusion, much like the American dream. Nick believes that Gatsby is "great," yet there is much that he is willing to overlook in his assessment of Gatsby's character (such as the fact that he actively pursues another man's wife).
- The setting: Gatsby believes that his mansion in West Egg will allow him access to Daisy and her lifestyle. Unfortunately, he fails to realize that a chasm exists between his setting and Daisy's home in East Egg, which favors old money. Despite achieving incredible wealth, Gatsby can never reach across the bay to Daisy's home in East Egg, because he can never be the man that Tom represents, supported by longtime family wealth. Gatsby is ultimately forced to confront the truth that he has been disillusioned regarding the acquisition of wealth and the power it can afford him.
- The symbolism of the bay: The bay that separates East and West Egg enforces a physical separation between Daisy and Gatsby. Several times, Gatsby is seen looking across that bay, longing to reach Daisy on the other side. Socially, he can never make the leap to East Egg, demonstrating the impossibility of fully realizing his ultimate dream.
- Imagery of light and whiteness: When Nick visits Daisy's home, she and Jordan are enveloped in whiteness, often associated with innocence. Of course, neither of these women is particularly angelic, so the appearance of innocence is misleading. When Tom and Nick stop by Wilson's station, Myrtle "block[s] out the light from the office door," which symbolizes her efforts to hide the truth. When Nick attends Gatsby's party in chapter 3, there are numerous references to the way the light changes. When Daisy appears at Gatsby's house, he points out to her that the "whole front of it catches the light." Light and whiteness can symbolize truth, innocence, and goodness. Of course, their usages prove ironic as Daisy ultimately rejects Gatsby's pursuit of her. This isn't a novel of truth and goodness but of deception and lies.
- The symbolism of Gatsby's mansion: Although intentionally chosen to demonstrate that he is worthy of Daisy, Gatsby is very much alone in his estate. He has no close friends besides Nick, and many people who attend his lavish parties don't even know him. This reveals a hard truth about the American dream: Sometimes the sacrifices people make to achieve a lifestyle of splendor don't create meaningful relationships. In the end, Gatsby dies alone, and none of the partygoers care enough to even attend his funeral.
- If you need further ideas, you could examine the characterization of Daisy (Isn't it interesting that her very name connotes an innocence and purity that stands in sharp contrast to her character?), the symbolism of cars (Gatsby's Rolls-Royce, a symbol of wealth and vanity, both carries people to Gatsby's parties and kills Myrtle), and the symbolism of clocks and time (Gatsby fails to realize that Daisy has moved on and can never be his again; time has forever separated them).