How does F. Scott Fitzgerald portray the American Dream in The Great Gatsby through his use of symbolism and other literary devices?

Fitzgerald portrays the American Dream through the lyrical language of Nick Carraway but also shows it in the novel as having been debased. In a famous passage, Nick refers to the American Dream as follows: 

Gradually I became aware of the old island here that flowered once for Dutch sailors’ eyes—a fresh, green breast of the new world.… For a transitory enchanted moment man must have held his breath in the presence of this continent, compelled into an aesthetic contemplation he neither understood nor desired, face to face for the last time in history with something commensurate to his capacity for wonder.

The symbol of the American dream, a dream of being able to start anew, is the "fresh, green breast of the new world." The new world is pure: fresh and green, with green here meaning young and untouched, as well as fertile. This links us to Gatsby's dream of recapturing a purer past with Daisy, when they were both younger and fresher. For Gatsby, the dream is also symbolized by the color green, particularly by the "green light" at the end of the pier representing Gatsby's desire for Daisy.

Nick's lyrical language accentuates the beauty of the dream (even if the reality is more sordid: the story of the novel shows the reality while Nick's lyrical prose conveys the dream). Nick doesn't use ordinary, everyday words but heightened prose, such as  "transitory, enchanted moment," that along with the image of "man" holding his breath, underscores the fragile, ephemeral nature of the American dream. The poetic nature of the dream is highlighted in the last lines of the passage as well, with the alliterative, rhythmic use of words beginning with "c." 

At the very end of the book, the dream is again symbolized as the "green light" and the dreamers identified with the vivid image of "boats against the current," pulled back into the past.