When one writes a critical analysis of a poem or any literary work, one is making an argument about the meaning of the poem or work. To do this, one has to first analyze the piece. For a poem, it's best to break your analysis into three parts: structure, sound, and sense.
When looking at a poem's structure, what we are doing is looking at how the poem is constructed. How long is the poem? Is it broken up into stanzas? how many lines per stanza? Looking at structure can help our analysis because different poetry types have different structures and a poetry type can help define a poem's meaning. For example a sonnet is typically 14 lines long with a rhyming couplet at the end. A sonnet also follows a typical rhyme scheme. Sonnets are also known to refer to specific subject matters, such as love, religion, and even politics. So recognizing that a poem is a sonnet can also help you recognize the subject matter of the poem. While the poem "The Orphan Girl" is not a sonnet, it certainly does have a strict structure of being broken up into two stanzas. Why break it up into two stanzas? Does each stanza focus on a specific part of the story? The first stanza appears to focus on a description of both the girl and her parents, as well as what happened to both parents, while the second stanza focuses on a description of what will happen to the poor little girl now that both of her parents are deceased.
When we refer to sound, we refer to not just the rhyme scheme, but any emphasis a writer can create through repetition, such as alliteration, consonance, or assonance (Dr. Wheeler, "Schemes: Repeating Yourself"). This poem in particular has a very interesting rhyme scheme. We analyze rhyme scheme by designating each rhyming word with a letter name, so that we can easily see the patterns. This poem starts out with an ABAB pattern but then switches to a BBCC pattern continuing in this vein all the way down to MM. The four ABAB lines specifically describe the beauty of the little girl, making the reader empathize even more with her pain and her plight. We see the description of the child's beauty in the opening lines:
Her hair was black as a raven's wings,
Her cheek the tulip's hue did wear,
Her voice was soft as when night winds sing,
Her brow was as a moonbeam fair.
Once the poem has been analyzed for many different details, we can derive a deeper sense of the meaning of the poem. Essentially, the poem describes an orphaned girl who will now be "scorned" by the world unless she is "sheltered" by some caring person.