In a critical appreciation, you should look at a poem with a discerning eye, decide whether or not it is an effective poem, and then explain your decision. To write a critical appreciation of Coleridge's "Frost at Midnight," then, your first step is to read the poem carefully several times, and don't just read it casually. Pay close attention to its language, imagery, and meaning.
Now try to determine the poem's purpose. Think about why Coleridge has written this poem and what he is trying to express. It seems that he is meditating on silence and solitude, the inability of one's thoughts to ever be completely still, the desire for connection with other human beings, and the communication of God through the natural world. These are the concerns of a Romantic poet, which, of course, Coleridge is.
At this point, you need to determine how well Coleridge has achieved this purpose and how he has done it. This is the section of your critical appreciation in which you explain the poem's merits and failures (if any). You might talk about the poem's form, rhyme scheme, which is blank verse (i.e., no rhyme), and strict rhythm, in this case, iambic pentameter. This seems well suited to the meditative tone of the poem, for it allows free expression of ideas in a soft, almost swaying rhythm that reflects the flicker of firelight.
You might also talk about the poem's extensive imagery, which serves to enhance Coleridge's ideas. We can easily picture the flickering light, the sleeping baby, the school scene, and the natural settings. Coleridge uses these images as starting points to reflect on his main ideas. His meditation on the baby, for instance, leads him to think about what he wants the child to experience, namely the "eternal language" that God uses to speak through nature and the sweetness of all seasons.
Your critical appreciation might also touch on how these ideas resonate (or not) with you personally. If you have ever experienced such interactions with nature or perhaps the silence that is so silent that it is actually disturbing, then you have a first-hand idea of what the poet is talking about and you can better appreciate the poem. Even if you have not had such experiences, you might write about how the poem has encouraged you to be more mindful of such things in the future.