Particularly if you're new to poetry, the best approach to take when reading a poem is to start small and work your way up to its deeper meanings. Here are some basic questions you'll want to ask yourself, which build upon one another:
1. What is happening in the poem?
Literally: What is the poem’s action?
Figuratively: What metaphors drive the poem’s message?
2. Comment on the poem’s music: What do you hear in this poem?
the poet’s voice, the language used
use of rhyme and near rhyme
the poem’s rhythms, its cadence, its momentum
use of alliteration and assonance
performative enjambments (line breaks)
(All of these elements add emphasis to certain words, images and ideas. Why?)
3. Are there any memorable images? What do you see in this poem?
4. What general themes does the poet touch upon?
5. Ultimately, what is the poet/poem trying to say?
If you want a more detailed evaluative rubric, I'm quite fond of the method proposed by Ann Lauterbach in an interview in Daniel Kane's book, What is Poetry: Conversations with the American Avant-Garde:
DK: Is there a method or series of steps that you might recommend teachers to take in presenting "On (Open)" [a poem of Lauterbach's they'd been discussing] to high school students not so familiar with poetry?
AL: A poem is not a puzzle to be solved. A poem is an experience, an event, in and of language. It should be approached as such:
What kind of event happened to you when you read this poem?
Did you get a feeling?
Did you have an idea?
Did you get reminded of something?
Did you go elsewhere, away from the familiar world into another, stranger, one?
Did you look up words and find out new meanings, as you would ask directions in a strange city?
Why do you think the poet made this word choice, and not another?
Why do you think the line is broken here, at this word, and not at another?
How is a line break in a poem different from a comma or a period in a prose sentence?
When making a short quotation from a poem, don't type it out as it appears on the page, but rather use slashes ( / ) to indicate line breaks (a.k.a. enjambments), and double-slashes ( // ) to indicate stanza breaks, like so:
Paul Blackburn's stanza below from "The One Night Stand : An Approach to the Bridge"
New day's sunWould be presented like so: In "The One Night Stand : An Approach to the Bridge," Blackburn paints a lovely portrait of early morning in the city, in which the "New day's sun / doubles itself in the river" and "[a] double string of blue lights /glares to mark the bridge."
doubles itself in the river
A double string of blue lights
glares to mark the bridge, the
city huddles under a yellow light
the sodium flares
gleam under oblique
sun's double in the stream,
Likewise, if one were to quote from this portion of Philip Whalen's "The Same Old Jazz,"
While I imagine whatever I imagine
dry stalks of yarrow,
repeated Y-branching V's, a multiplication
Of antelope, deer-horns? Umbels
Hairy brown stars at the tip of brown wires
A menorah, or more learnedly, "hand" written in Great Seal Script
It might read like this: Whalen's "whatever I imagine" includes a litany of natural imagery, such as "[w]eed / dry stalks of yarrow, / repeated Y-branching V's, [and] a multiplication // [o]f antelope, deer-horns."
Please also remember that though traditional MLA rules for citations indicate that you must give the line number(s) for your quotations and paraphrases, I think that's a little draconian, and so just giving the page number(s) will be fine.