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, , symbolism, , 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.