When one writes a critical appreciation of a text, it is important to suss out the text's meaning or central purpose; ask yourself, why did the author write this? What is he or she trying to convey? Furthermore, a critical appreciation aims to figure out how the author achieves this meaning or purpose and ultimately analyzes how effective is the text in conveying this meaning.
It can also help to consider the historical context of the text. For example, this poem was published in 1918, written by a man who served in the Royal Welsh Fusiliers in World War I. He was critical of the war and of the government that he felt had prolonged the conflict. This helps to account for the incredibly dark and disapproving mood of the poem.
The text depicts a once-blithe young man who is sent to war and suffers cruelly in the trenches and who subsequently takes his life. Finally, the speaker directly addresses and criticizes those who cheer soldiers as they march off to war because he knows the terrible fate that awaits these young men. The poem uses a regular rhythm, called iambic tetrameter, perhaps mimicking the sound of marching. Here's an example (with the stressed sounds in bold and a "/" to divide feet from one another):
I knew / a sim / ple sol / dier boy
Who grinned / at life / in emp / ty joy
It also makes use of rhyming couplets (each pair of lines ends with words that rhyme: boy and joy, dark and lark, etc.), possibly emphasizing the inevitability of soldiers' loss of innocence and happiness by setting up predictable rhythm and rhyme-schemes.
The speaker also directly addresses those individuals who cheer for soldiers who are marching to war, using a technique called apostrophe, which really drives home his criticism of war by drawing attention to how so many of us romanticize and encourage these wrong-headed views of it. Sassoon uses these poetic devices in order to launch his criticism of war and draw attention to the enormous toll it takes on those individuals who are forced to participate.
Now, how effective do you think his criticism is? Are you affected by the poem? Why? Does it tug at your heartstrings? If so, this is likely the result of the poem's mood. Perhaps you are surprised that such a dark poem sounds so bouncy and sing-song? If so, this is likely the result of the poem's rhythm and rhyme; you can even discuss the irony of these choices. It sounds like a nursery rhyme, doesn't it? But should it? It has such an upsetting topic: a young man who takes his life.
This discrepancy between what the poem might encourage us to expect and what actually happens is called irony, and irony is often used to point out social flaws. Consider how much the poem affects you, and then try to figure out why.