A good place to begin would be to establish what the American Dream had been before the 1920s, the time period of the novel. Then you could examine the factors that had corrupted the original American Dream, as they are developed in the novel. Finally, you could discuss the results--how American society had been affected by the bankruptcy of the American Dream. Organizing an essay in these three sections would provide an outline for you to follow in examining the primary theme in the novel, that the American Dream had been corrupted by materialism, leaving a society awash in selfishness and immorality.
To establish what the American Dream had once been, examine Gatsby's dreams while he was growing up in North Dakota. These are brought into the novel at its conclusion when his father shows up for the funeral and brings with him the book his son kept in which he listed his "resolves" and recorded his daily schedule. These notations show that Gatsby, who had been born Jimmy Gatz, worked hard and tried to better himself--surely elements in the original American Dream. Also, the final passage in the novel when Nick imagines how American looked to the first settlers and describes the new land as they perceived it would be excellent support:
I became aware of the old island here that flowered once for Dutch sailors' eyes--a fresh, green breast of the new world. Its vanished trees, the trees that had made way for Gatsby's house, had once pandered in whispers to the last and greatest of all human dreams . . . .
Nick's reference to "the last and greatest of all human dreams" implies what made up the American Dream in its beginnings--a dream of freedom and personal fulfillment.
The primary force that corrupted the American Dream, as Fitzgerald presents it, is the force of materialism. The novel is filled with passages to show the accumulation of material possessions and the many displays of wealth. Descriptions of the Buchanans' fine estate and Gatsby's huge mansion and various fine possessions would provide many quotations to support the idea that materialism is the primary value of the time.
Finally, to discuss the corruption of the American Dream in terms of its impact on society, as Fitzgerald presents it, look to the characters' lives. Tom and Daisy are clearly immoral; Gatsby lives a life of crime to amass his fortune; and Gatsby, Myrtle, and George all die violent deaths. Tom and Daisy's moral bankruptcy is expressed by Nick in this passage:
They were careless people, Tom and Daisy--they smashed up things and creatures and then retreated back into their money or their vast carelessness or whatever it was that kept them together, and let other people clean up the mess they had made . . .
Through Tom and Daisy's behavior and through Gatsby's life and death, Fitzgerald shows how far apart society in the 1920s has grown from the values inherent in the original American Dream.
The links below will take you to several eNotes resources that should be very helpful as you write your essay. Good luck!