Fitzgerald portrays the Jazz Age in The Great Gatsby in a variety of ways.
First, he sets Gatsby's parties as great dance and drinking parties. Throughout the night, he references music. Here are just a few descriptors during the first party Nick attends:
By seven o'clock the orchestra has arrived, no thin five piece affair, but a whole pitful of oboes and trombones and saxophones and viols and cornets and piccolos, and low and high drums...
The lights grow brighter as the earth lurches away from the sun, and now the orchestra is playing yellow cocktail music, and the opera of voices pitches a key higher...
Suddenly one of these gypsies, in trembling opal, seizes a cocktail out of the air, dumps it down for courage and, moving her hands like Frisco, dances out alone on the canvas platform. A momentary hush; the orchestra leader varies his rhythym obligingly for her, and there is a burst of chatter... The party has begun. (Chapter 3)
The parties are set to the backdrop of the Jazz Age.
Later in the book, when Daisy goes to a Gatsby party, she is excited to meet all the famous people and to dance with Gatsby. (Chapter 6)
Throughout the book, the themes of the Jazz Age are protrayed through the characters. Fame and fortune were new for many aspiring artists and the popularity of Jazz made it regular for the common people to meet some of these artists. Readers see this attitude particularly through the female characters. Jordan, although low-key, certainly keeps up on the gossip of famous people, while Daisy is just attracted to knowing all of the interesting and cultured people after being cooped up in her relationship with Tom.