A Marxist reading is one where you are paying attention to the construct of class in a text. Marxism assumes that societies work best when everyone is working collectively for the betterment of that society, and that competition between people doesn't necessarily lead to improvement. Marxism suggests that capitalist societies do not function well because there is an inevitable conflict between the working masses (the proletariat) who produce, and the individuals or corporations who reap the rewards of their labour.
Reading a text in this way would foreground ideas such as
the way a class divide has been constructed, with one group privileged over others.
the way that those with capital (money, resources, abilities) are depicted in a particular way.
the way that those of the underclass may be portrayed as unaware of their place or perhaps as participating in their own subjugation.
the way that a text might be reflective of particular societies, cultures, or sub-cultures.
the way that work and social responsibility might be portrayed.
the different ways that people might be represented as being important to a community.
Some texts which might be useful to look at from this perspective are: The Handmaid's Tale - Margaret Atwood
In what ways could Offred's role in her society be seen as beneficial to the 'greater good'?
What class structures are in place in Gilead and what impact does this hierarchy have on its participants?
How is class determined in Gilead? Are the same markers of class present there as in our society? How are people marked out as belonging to each group?
Why might it be surprising that Offred would be considered so lowly in her community? What does this suggest about the way that class is determined?
1984 - George Orwell
How are the classes kept separate in Airstrip 1? What parts of culture are kept from the working class and why?
In what ways are Julia and Winston participating in their society's separation of classes?
The Harry Potter series - JK Rowling
What evidence is there of class divides in both the wizarding and muggle worlds?
In what way is the macro (wizards vs. muggles) and micro (within the wizarding world) class division problematic? Think about characters such as Stan Shunpike and Argus Filtch, as well as the Weasley family.
Who are the real proletariat (the working masses) in this series? How are they 'used and abused'? Are they aware of their position in society?
Once you've identified issues of class in a text, you must then incorporate them into the meaning you make. For example, JK Rowling's Harry Potter series, despite her creation of a world of magic and fantasy, is largely reflective of our own Western capitalist ideologies which promote division, competition, and the marginalisation of those who are weaker or poorer.
Margaret Atwood's The Handmaids Tale is generally read as a lament on the way that Second Wave feminism threatened to undo the good work of past feminist movements, stripping women of their rights. However, reading from a Marxist perspective, it could be argued that despite her lack of personal satisfaction, Offred is only asked to contribute to her community in the best way she can, and that her failure to do so is unfortunate and selfish.