This long period of six weeks for the assignment allows for successive drafts to be worded and edited in seminar; both with peers and with the tutorial leader.
"Close Reading" in our context means reading the text carefully, paying attention first and carefully (i.e. closely) to the words and phrases: their diction, etymology, associations, order, meter, rhyme, metaphors, and the like. Close reading a text is to concentrate start on the particular before making remark on the general; letting, as far as possible, the text speak to you before you speak to the text.
When you have made been through the text and made notes and comments about this level of specific detail, you then write these discoveries up into essay form, where you then consider any conclusions that appear to you about the author and his or her intentions and significance; historical, intellectual or æsthetic.
Consider the famous line, l.15, from Tennyson's "The Lady of Shalott,"
"Four gray walls, and four gray towers"What does the first "four" give us? With "walls" we have a image of imprisonment. The four right angles implied invokes rationalism: closed rather than open, and thus associated with controlling masculinity (cf. Gaskell's Cranford.) This masculine element of the enclosure is strengthened by the phallic "four....towers": alluding perhaps to four levels of men (incl. lover) The "four" additionally suggests enclosure for the four points of the compass. It is also a sharply non-religious number: odd additional from the sacred number three. It is also the number of iambs in the line. The second word, "gray," denotes colourlessness, which is a direct contrast with the vivid colour-words in the stanzas immediately surrounding (e.g. "blue," "yellow," "red.") Gray also has a moral connotation of being neither openly good (white) nor openly bad (black.) "Gray" is the colour of ambiguity, which sets up the quality of the Lady's ambiguous action in leaving the tower.
That certainly is the beginning of a close reading of this one line (e.g. further work on the structure of the line's parallel clauses has intriguing relevancy.) It is just to illustrate the level of detail that a close reading has. And of course your own close reading will likely differ from this: a student once pointed out that l.485 of bk.2 of Aurora Leigh--'life develops from within'--adds a maternal dimension to the passage: a reading which, you won't be surprised to hear, had hitherto evaded me.