A critical appreciation or a critical analysis of a poem should address content and form. In discussing content, the critic should describe what the poem is about, possibly noting an author's intent, and/or noting different interpretations of the poem's meaning.
In discussing form, the critic should address literary techniques and literary elements. Literary elements can be: structure, tone, rhyme scheme, meter, theme, and type or genre (love poem, elegy, pastoral, etc.) Literary techniques can be: personification, irony, paradox, hyperbole, metaphor, conceit, etc.
For purposes of answering a question of critical appreciation on Enotes, try to address issues of content and form while addressing at least two literary techniques and two literary elements.
For example, if the poem is Robert Frost's "The Road Not Taken," address the content: the poem is about choices. Literary elements: talk about the rhyme scheme (abaab) and the tone (solemn, looking back). Then talk about the literary elements. The poem is an extended metaphor describing two roads in the woods but as metaphors of choices in life. Frost is also ironic: the speaker claims to have taken the road "less traveled by" but in fact, he took a road that looked the same as the other.
To write a critical analysis of a poem, first discuss the poetic techniques the poet uses, then discuss the poem's meaning, both the denotation and the connotation. Finally, discuss how the poetic techniques reinforce the poem's meaning.
When you discuss the poet's techniques, you will want to comment on the rhythm, rhyme scheme, and meter. Traditional verse often uses standard rhythms such as iambic (alternate syllables are stressed beginning with the second syllable of the line) or trochaic (alternate syllables are stressed beginning with the first syllable of a line). To determine this, you may need to perform a scansion of the entire poem, noting the stressed and unstressed syllables. This will allow you to see how consistent the rhythm is. Meter refers to the number of feet (repeated syllable groups) in a line, such as trimeter (three), tetrameter (four), and pentameter (five). To determine the rhyme scheme, assign a new letter of the alphabet to each line that does not rhyme with a previous line, and label rhyming lines with the same letter. Note any repetitive patterns, for example, if the rhymes from one stanza interlock with those of the next stanza. Other poetic techniques include alliteration, consonance, assonance,personification, similes, metaphors, and symbols.
When discussing the meaning of the poem, first think about its denotation, or face value meaning. For example, William Wordsworth's "We Are Seven" is about the persona's conversation with a young girl whose siblings have died but whom she continues to number among her family members. Then consider the connotation, or deeper meaning. This will include the theme of the poem---the message or universal truth it conveys. This gets subjective, but as long as you can support your opinion from the text of the poem, your ideas are valid. Connotations of "We Are Seven" might include that children deal with death better than adults do, or that even death cannot separate people who truly love each other.
Finally, attempt to connect the poet's techniques with the poem's message. In "We Are Seven," the iambic rhythm, short lines, and consistent rhyme scheme convey a sing-songy happy feeling that reinforces Wordsworth's depiction of the innocent faith of childhood. A poet who is trying to convey a calm and peaceful mood may use a lot of alliteration and consonance that repeats the soothing /l/ and /s/ sounds, as Wordsworth does in "I Wandered Lonely as a Cloud." On the other hand, a poet who wants to convey the harsh reality of war, as Wilfred Owen does in "Dulce et Decorum Est," may use alliteration and consonance emphasizing the guttural sounds such as /k/ and /g/.
Analyzing the poetic techniques and the meaning of the poem and then tying together the techniques with the meaning will result in a thorough critical analysis of the poem.