Psychoanalytic literary criticism is the application of one or more psychoanalytic theories to literature, for example, the theories of Freud or Jung. Lacan and Adler are two others whose theories are used for literary criticism. Certainly, an author can be the focus of this kind of criticism, as can the reading audience. In many instances, though, only the text is used. When one is assigned to conduct psychoanalytic literary analysis, unless there is a specific requirement that the author be part of that analysis, I am aware of no reason that it would be necessary.
No matter what the focus is, the idea is that the analysis is performed through the lens of one or more theories. For example, if you are analyzing a literary text, you might discuss Freud's stages of development in the various characters or whether the characters are operating on their egos, ids, or superegos. From another perspective, you might inquire what Jungian archetypes characters in a novel represent. The works of Roberson Davies are frequently analyzed using Jungian principles. If you were analyzing the author of Peter Pan, J.M. Barrie, you might be speculating as to whether Barrie exemplified Freud's notion of arrested development. If audience analysis is of interest to you, you might want to consider the audience of the Twilight series, which could be easily analyzed with Freudian or Jungian concepts.
For a class assignment, it is always best to seek clarification of what the expectations are, but there is no requirement to analyze all three aspects, author, audience, and text, for this kind of criticism.