In reality the ways of approaching the task of how to read any work of literature vary as widely as the number of readers of that particular work. For scholastic purposes--in general achieving a greater understanding of all the aspects of a work of art--the most common methods are grouped into the following categories, or their respective sub-groups:
Focuses on the effect that differences and similarities between the respective circumstances of males and females in society has on specific works of literature and the art in general.
See: feminist criticism, homosexual criticism
Studies the effects that material conditions of various societies have on relative works of literature, with the general purpose of exposing the dependency of art on basic needs.
See: socialist criticism, cultural materialism, post-marxist criticism
Through analysis of imagery, themes, and structures within a literary work, this type of criticism aims to show that literature is always structured by complex and often contradictory human desires.
See: psychological criticism, freudian theory
In the reader-response critical approach, the primary focus falls on the reader and the process of reading rather than on the author or the text.
Utterly dependent on postmodern theory in general, the theory of literary interpretation challenges anything presuming to explain the major precepts of a specific work in a straightforward fashion. Instead, it shows how texts are often self-contradicting and prismatic
See: Jacques Derrida
This school is very similar to Marxism, except in that (as mentioned above) Marxism tends to focus on the 'bottom rung' of the social ladder, whereas New Historicism looks to the top of the social hierarchy. New Historicists also tend to draw on the disciplines of political science and anthropology given their interest in governments, institutions, and culture.
See: postcolonial criticism, Old Historicism
Formalists tend to see the text as a work of art and thus worthy of study as an object in its own right, distinctly apart from whatever particular socity, culture, or even individula artist that created it. They focus on the intrinsic elements and their inherent meaning and order.
See: narratology, structuralism
Please let me know if you believe I have left out anything drastically important, or made any glaring errors in my glosses. Done from familiarty and reference to this handy site: http://www.sla.purdue.edu/academic/engl/theory/