This might seem to be an intimidating question, but you can tackle this question very efficiently if we break down the process in the following manner.

Read the given poem at least two times and try to grasp the theme.  It will be thematically related to a poem you have already studied.  Often it is explicitly stated.  Keeping that poem in mind while reading the given poem will help you better understand its meaning.

Some explanations of difficult words may be given at the end of the poem with the question.  If not, try to pick up the meanings from the context.  Even if you do not understand the poem fully, do not worry, because you will be able to write a satisfactory answer with the limited understanding if you follow the following steps.

Write the first paragraph introducing the two poems and their authors.  Talk about the theme of the poem you have already studied in one or two sentences.  Say how the given poem is comparable.

In the next one or two paragraphs talk about the themes of the poems.  Show how they are similar or different. Discuss the possible interpretations.  Instead of talking about one poem in a paragraph and then moving on to the other, compare them side by side in each paragraph.  Use quotations from the poems to substantiate your argument. If you find it difficult to identify or explore the themes, at least try a brief summary of both the poems.

In the next paragraph examine the tone and mood of the poem and how it is created by the poet. Some words that can describe the mood of a poem are happy, romantic, realistic, optimistic, pessimistic, gloomy, mournful, sorrowful, etc. Some words to talk about tone are serious, humorous, amused, angry, playful, cheerful, sad, gloomy, etc.  For a larger list go here.

Next talk about imagery and symbolism.  Compare and contrast the use of imagery and symbolism in the two poems.  For example, in "Mending Wall" there is the image of a wall that divides the two neighbours whereas in the poem "Neighbour" by Iain Crichton Smith there is the image of a stream that separates the neighbours.  One is manmade while the other is natural.  Analyse the use of imagery by picking examples and identifying them as Visual (sight), Auditory (sound), Olfactory (smell), Tactile (touch), Gustatory (taste) or Kinaesthetic (movement).

Finally evaluate the language, style and format to find similarities and differences.  Talk about the musical quality achieved by alliteration, assonance, rhyming words and rhyme scheme.  Identify the language used as simple, difficult, Old English, colloquial, or slang.  Compare and contrast the figures of speech used in both the poems like simile, metaphor, personification, hyperbole onomatopoeia etc.

In the concluding paragraph present your opinion about both the poems.  You can use your own ideas and interpretations and speak about what effect both the poems have had on you.  If there is a message that you get from the poems, use that to finish your concluding paragraph with.

This is not a strict formula for writing comparative appreciation. This is just a bare skeleton.  Use your brilliance on top of it.