Catherine Murphy from Santa Clara University has a nice, concise overview of narrative criticism on her informative website:

Literary criticism is a broad term encompassing several different approaches to the literary text.  In the early days of historical criticism, the term was used for any form of close reading of the text, and thus could encompass form and source criticisms.  But since the 1960s, with the burgeoning of the field of literary criticism in the disciplines of English and World Literature, the term “Literary Criticism” in biblical studies has come to refer to approaches undertaken in these other disciplines.
In general, all literary critical methods examine the final text of a given biblical book, as opposed to the origins of its parts.  The literary critic assumes that the author worked with sources, but also that the author composed a new account from these sources – an account that has literary integrity.  The critic may choose to focus attention on the text or the response of the intended readers, and then within these categories to focus still further, for example on semiotics or narrative structures.