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