How does one write a critical appreciation of a poem?
A critical appreciation of a poem requires of one to analyse the poem as a whole and critically provide insight into the elements which make up the poem, such as diction, imagery, structure, rhyme, rhythm, the overall message or theme of the poem or the purpose of the poet. One should also be able to determine the context and setting of the poem and its relevance to the period in which it was composed and how it relates to the current context. Furthermore, one has to mention how and why the above-mentioned elements are either effective or not - this is the 'critical' aspect of one's discussion.
Obviously one has to apply the structural requirements for an essay - i.e. an introduction, body and conclusion. Furthermore, the requirements for proper punctuation, grammar and language, should be followed.
One needs to mention in the introduction the purpose of the essay through a thesis statement,discuss the various elements of the poem in separate paragraphs and conclude by either restating the thesis and the purpose of the essay or in some way requiring of the reader to make an assessment of your attempt or both. However the conclusion is worded, there should be a definite indication that the essay has reached its end.
The above answers give good insights, but as you can imagine, there is no one way to appreciate or analyze a poem. In other words, there are many ways in which to approach a poem. In light of this, let me give you a few different ways.
First, if you focus on the mechanics of a poem by examining poetic devices, you should also ask yourself what these devices do for the meaning of the poem. For example, the meter of The Tyger by William Blake reminds the reader of the incessant pounding of a hammer on an anvil. In this way, the poetic elements add to the meaning of the work.
Second, you should also focus on the historical context. For example, the Roman poet Horace writes ode 1.2 in the context of the flooding of the Tiber River. This act can be seen as a bad omen of what is to follow, or he can interpret it as the signaling of a new age with the rise of Augustus. In this way, he is saying the poet has a lot of power to interpret events in poetry for the general populous.
In conclusion, to analyze poetry, use as many tools and ways of reading as you can. That is critical.
In this context, “critical” means paying attention to the elements of construction – rhyme scheme, meter, stanza arrangement, imagery, etc. – that give the poem its balance, beauty, and effectiveness. Writing an “appreciation” requires a dissection of the way the poet has achieved his/her effects, and should be constructed like any essay – introduction, body, conclusion, paying particular attention to those elements that give poetry its signature – succinctness, “concentrated word magic.” If other poems by the same poet are known, you may discuss how this poem differs from or emulates the poet’s “normal” style; in a longer appreciation, you may also discuss the “age” or “style” of the poem – Romantic, Victorian, etc. -- and you might discuss the generic style – sonnet, ode, etc.