Marxist literary criticism attempts to read texts for discovery of (1) reference, direct or indirect, to oppression of the working classes by the privileged class and for the disclosure of (2) the economic situation at the time the text was written. What this means in terms of Pride and Prejudice is that a Marxist critic would read to find evidence of oppressed alienation of workers, for example, domestic staff, and for indications of the economic conditions in the text and during Austen's writing years, spanning from the late 1790s to the early 1810s, as she finished writing Pride and Prejudice in 1798 while it was not until 1813 that it found a publisher (recall that the text was not modified to reflect socio-economic changes, if any, that may have occurred in the 15 year span).
The analytical tools used by a Marxist critic in a Marxist reading are examination of the text for indications of economic oppression of workers; alienation (estrangement) of workers from their creative selves, from other workers, from the products they make, and from the creative process that their labor advances but that is not under their control; economic exploitation by the upper classes resulting in conflict between classes.
Other analytical tools used are examination of the text for indications--related to the text and related to the author's own time period--of the economic base and superstructure, ideology and hegemony, and reification of workers. The economic base is the economic principles that establish the social and cultural order of things, which is called the superstructure and which includes such as religion, education, law, and art. Ideology is a belief shared by all (or most) in a society about the way things should be that grows up out of the superstructure, which is itself determined by the economic base. Hegemony is a collection of such ideological beliefs.