What is Formalist criticism?

Formalist criticism is one way that a reader can approach
his understanding of a text.  When a reader looks at a poem, play, story or novel from a
formalist perspective, he is looking solely at the work as something to be dissected, so
he looks for all of the literary techniques and devices that an author uses to create
the text and its meaning.  He does NOT look at the author's life, he does NOT consider
the text from a historical or psychological perspective; he does NOT consider how this
text is like other texts -- those are all other modes of literary
criticism.

Think of "Twinkle Twinkle" as an example.  With
formalist criticism the reader would notice the repetition of the word twinkle and
consider connotation and denotation of the word.  It would notice the first person
speaker of the poem.  He would note the use of simile in the 4th line (like a diamond in
the sky). He would note the refrain of the first two lines in lines 5 and 6, and he
would mark the meter and the ryhme scheme.  Once the poem was literarily dissected, then
the reader can consider how those elements work together to create the meaning of the
poem as a whole. 

You can read more about this mode of
criticism at the site listed below.