What are some contexts of Siegfried Sassoon's poem "Suicide in the Trenches"?

The most important context for Siegfried Sassoon’s poem “Suicide in the Trenches” is the fact that it was written during (and about) World War I. Although wars have obviously existed for millennia, World War I was an especially destructive and horrible conflict, partly because so much of it involved digging and defending trenches, so that forward movements in battles often involved just yards of progress (if that) and partly because the war involved such stunning innovations as air planes, massive artillery pieces, tanks, and (most grimly) the use of poison gas. Literally millions of people died in this war. Europe had never seen anything like it before. “Suicide in the Trenches” was first published early in 1918, when the full horrors of the war had become obvious to practically everyone involved.

By the point, Sassoon, although himself a soldier who had volunteered for service in 1914, had come out against the war. His younger brother had perished in the conflict in 1915 -- a great loss to Sassoon. Sassoon’s own poetry became darker and grimmer as the war progressed; he tried to convey realistically the lives, deaths, and sufferings of the soldiers caught up in the conflict. He displayed great personal bravery in battle, and in fact his almost reckless fearlessness might itself be seen as a means of both defying and tempting death. Sassoon, in other words, may have been able to identify with the suicidal feelings that finally take the life of the soldier described in his poem. Eventually Sassoon openly attacked the war and defied his superiors. By the time he wrote “Suicide in the Trenches,” Sassoon had come to feel strong contempt for those whose only involvement in war involved applauding the troops who actually had to fight:

You smug-faced crowds with kindling eye 
Who cheer when soldier lads march by, 
Sneak home and pray you'll never know 
The hell where youth and laughter go.

Patrick Campbell’s book on Sassoon’s war poetry gives a very helpful account of the background of this particular work. He suggests that the poem shows the influence of A. E. Housman, a major English poet of the day, and that it also reveals the impact of the ballad tradition in English verse.

What is the presentation of Siegfried Sassoon's poem "Suicide in the Trenches?"

As for structure, you have 3 stanzas following the rhyming pattern of AA/BB, meaning, lines A rhyme and lines B rhyme.  As for content, stanza one describes a happy, cheerful young lad.  Stanza two throws us the bad news:  war has turned the happy young lad into a miserable man, who chooses suicide over surviving one more day in the awful trenches of war.  The blunt presentation of that action, "He put a bullet through his brain", makes the reality of it seem even more harsh.  Stanza three speaks to "You snug-faced crowds with kindling eye/Who cheer when soldier lads march by", rebuking them, telling them to "Sneak home and pray you'll never know/The hell where youth and laughter go."

It's a rather straightforward, heart-wrenching poem that directly confronts the horrors of war.  The last stanza really drives it home, contrasting the cheering crowds to the brutal reality, the "hell" that war can be.