A number of methods of characterization are used in The Great Gatsby.
Characters are defined both directly and indirectly. Nick offers direct character analysis of almost every major character, from Daisy to Jordan to Gatsby, Tom and Myrtle. The language of this direct characterization is essentially the same kind of language used in "everyday life" to describe a person's personality.
Another mode of direct characterization that comes from Nick is a physical description of each character, usually offered at the first meeting with a character. One example of this is the use of the phrase "slender" repeatedly to describe Jordan in the first chapter.
Characters are also given indirect definition through dialogue and action, with certain phrases and actions being presented as characterization (not related to plot, theme, or atmosphere). We can see these type of characterization with the description of Gatbsy's odd gesture at the end of the first chapter (reaching across the water) and in his repeated phrases ("old sport" and his false Oxford-isms).