How can we analyze a poem or a text from a Russian formalist approach?
In order to answer this question we have to consider the origins of the formalist approach in literary criticism. The Russian Formalism emerged in Russia in the early 1920s. The main figure was Roman Jakobson. The formalists were solely concerned with the form of a literary text; hence the word formalism soon gained a pejorative meaning to imply “limitation”.
The concern about form was indeed primordial to analyse a text and terms like sjuzet (the plot), and fabula (the story) became inherent in the Russian Formalism. The former refers to the order and manner in which events are presented in a narrative, whereas the later pertains to the chronological sequence of events.
To analyse a text according to the Formalists one should focus on the text itself and forget all sorts of external sources that might refer to the literary work. Thus, the historic and social context, the author’ intentions and how the text affects readers are irrelevant. Instead, we should concentrate on every single element of the literary work.
Furthermore, the formalists came with the term “defamiliarization”, which means that works only have a literary value if they differ from ordinary language. Works have an alien language which can only be deciphered through a careful close reading. So, the role of the critic is to decipher this “estranged” language by paying attention to all sorts of figurative language. This includes paradoxes, irony, tensions within the text and possible ambiguities. Those are important elements that pertain to sjuzet. Another relevant aspect is that sjuzet may not coincide with fabula. It all depends on how the events of the story are told in chronological order.
Source: "Dictionary of Literary terms and Literary theory"-Penguin Reference