How do I write a critical appreciation of a poem? What are the components?
It depends on what your professor stipulates as the length for the final draft - but if this is a 2-5 page typed paper, I would say focus on three categories of criticism. Think about this as your typical 5-paragraph essay - most good analysis is organized into three chunks - but instead of only devoting one paragraph to each category - feel free to write more.
As far as the "parts" of critical appreciation go - you have almost endless options with this. You can approach it from the "What are other people saying?" route - where this paper is actually more of a research paper than a personal analysis - but your own assessment is intertwined in how you present your information.
If outside sources are not required than likely your professor wants only personal analysis. Here, you rely on what you learned in high school English: literary elements and rhetorical techniques. What is this poem trying to say and how effectively does it say it?
I'd say good critical analysis combines any two of the following: tone/attitude, theme, and literary techniques (things like figurative language, point-of-view, irony, symbolism, imagery, etc.) You can look at one main theme of the poem and analyze 3 different techniques used to portray this theme. You can analyze the overall tone of the poem and look at the different themes expolored through one tone. Do you see how the combinations can be played in different ways?
So again, while the exact structure of the 5 paragraph essay may not be quite enough, use it as the framework to explore the poem in 3 categories - just make sure the 3 categories all revolve around a common focus (thesis). The order of presentation (no matter how many paragraphs are devoted to each category) is best as follows: 2nd strongest point, weakest point, strongest point.
Hope that helps.