Approach the text with an eye for how the characters interact. Marxist thought relies on relationships between individuals, and even those aspects of relationships that are 'social' can be part of a Marxist critique.
Evaluate the vocational roles of all characters. The Marxist critique includes a focus on a "class system" where the vocations of characters provide the most direct reference to their place within this system. Look at the level of luxury that each individual has and how much they have to work.
Look at how characters use their free time. Part of the Marxist critique is based on the argument that individuals can use free time productively. Examining the free choices of individuals is actually a large part of Marxist literary criticism.
Assess the role of government in the piece of literature. Is it draconian? Laissez-faire? Marxist thought relies on government as a model for liberty and also for communalism: look at the tools that government uses. Does the government, in soliciting citizenship, appeal to the capitalist tendencies of individuals or to their innate love of community?
Use Marxist writers as a guide. Pick ideas outlined by Marxist writers of past eras and apply them to your particular study.