I think you are asking how to go about writing an essay that explores a critical appreciation of a poem, so I will make a few suggestions to help you complete this kind of literary task.
The first thing to note is that your task to write a "critical" appreciation. This means that your essay must go beyond your personal response to or appreciation of the poem. You may like the poem, but explaining why you liked it or how you think it relates to your life is not your task. Instead, you need to read and consider the poem with a critical, literary eye. Your ultimate goal is to understand the poem and to write an essay that explains how the various literary techniques used in the poem help to convey its meaning.
Here is what you will need to do:
1. Read the poem aloud to yourself and with a pen in your hand. As you read it, underline anything that strikes you in any way: figurative language, imagery, sound devices, diction, punctuation, allusion, etc.
2. Read it again, and add some comments near the parts you already underlined. You comments could be an identificiation of a literary device, a question raised by the poem, a word(s) that name the tone. You should also be mentally paraphrasing the poem as you go. Be sure you understand who the speaker is and what the dramatic situation of the poem is.
3. Read it again and draw lines through the poem in places where it makes sense to create manageable "chunks." These lines may or may not be at the stanza breaks (if there are any).
4. Now that you have read the poem several times you should have a good understanding of it, so it is time to create a thesis statement. Your thesis statement can be on any aspect of the poem you would like to discuss, but it is probably a good idea to argue an interpretation of the meaning of the poem as a whole, or its theme(s).
5. Next, plan your essay. What choices does the poet make that help to shape your overall impression of the poem's meaning? HOW do those devices work in the poem? These points will need to be organized in some logical fashion in your body paragraphs. You could organize your essay by literary devices, but it would probably be more logical and organic to write the poem in a chronological fashion. What are the most important or relevant devices at the beginning of the poem? the middle? the end?
6. Your conclusion should then make your ultimate point. What extension can you offer? Try to avoid merely repeating your introduction, your thesis, or the points of your body paragraphs. What can you say about what the poet accomplished by the way he wrote the poem? THAT will demonstrate your ultimate, critical appreciation of the poem.