There was not complete agreement among New Critics of the 20th century. Ransom supported New Criticism but did not like the New Critic tendencies of ignoring culture and history. However, in general, New Criticism was a theory of criticism largely focused on close reading. The typical New Critic analyzed form, content, and interplay between the two. Also typically, the New Critic ignored historical context, autobiographical information about the author, authorial intention and reader response. By ignoring all of these, the New Critic focused on the individual work itself, looking closely at its themes, metaphors, structure, genre, and other formal qualities.
So, taking a New Critical approach, don't concern yourself with author's intent, your own response (as a reader), or historical background. Look at the metaphors, recurring symbols, character types, structure of the story, language, etc. For example, look at themes like rebellion and manipulation and how these are presented in the characters' personalities, thoughts, and actions.
Note, that while a New Critic approach really helps zero in on the text itself, such an approach can always be supplemented by other critical approaches such as reader-response, New Historicism, etc.