The best starting point when writing a critical appreciation of a poem is to determine what the author's message or theme is. Once you determine this key point, the rest of the paper falls into place much easier.
I tell my students to next look at the author's tone. What is the author's attitude toward the subject of the poem? How do you know? What words do they use to convey that tone? You can then discuss how the tone is important to the theme of the poem.
It's important to then look for literary elements you're familiar with. Do you see a simile? What about great imagery? Is there an example of personification? Once you find these, the key point to remember is that the author made these poetic choices for a reason. How does that simile contribute to the tone or theme? How does the imagery utilized bring deeper significance to the tone or theme?
For example, in the poem "Because I could not stop for Death –," Emily Dickinson chooses to personify Death. Why does she make that choice? The image provides a way for her to discuss the transition into the afterlife as though she is a passenger in a carriage with Death. By doing so, she is able to reflect upon the life she's lived in light of the knowledge of death that all people face.
In the poem "Stopping by Woods on a Snowy Evening," Robert Frost uses imagery to convey the peaceful scene before him as he pauses in snow-filled woods on a dark evening. Why does he use imagery there? The peaceful imagery he utilizes contrasts with the "But" at the end of the poem; he has "promises to keep" and "miles to go" before he sleeps. He is in a hurry and doesn't have time to enjoy this peace often.
Each choice the poet makes is for a specific purpose. It's important, therefore, to not simply identify those literary elements but also to analyze how each one brings deeper significance to the author's work.