As was said by others, life in the trenches really sucked, if you even got that long to experience much of it...
Soldiers coped, or didn't cope, in a number of ways.
The first example was officially sanctioned. It was called the "Rum Ration". Before attacks, getting up and plodding toward the enemy's machine guns, the quartermasters would issue a large amount of cheap booze to "stiffen the troops's resolve". It wasn't uncommon for many of the soldiers to be stubling ahead, blitzed right out of their minds. Alcoholism was rampant throughout all armies, and many bunkers within a trenchline even had stills to produce their own vile booze.
The next example was to run away. Desertion was more of a national problem, or non-problem, though. Some north african units were completely unreliable, whereas Canadia and Australian units had very little of this happening.
Another answer was to refuse orders. This led to the curious position of "herder". This was a particular soldier, probably a sergeant, working with conscript units, who did not take part in the attacks directly, He remained in the "friendly"trenches to scare, threaten, or simply shoot any soldier who refused to do his duty.
The "self-inflicted wound" as someone else mentioned, was a relatively easy ticket out of the war, unless you were found out. Then you were likely to be patched up and sent right back to the front, put in prison, or even court-marshalled and executed.
Suicide was relatevely easy. You could easily commit suicide by enemy fire, and simply stick your head up over the trench. The traditional way of shooting yourself always works, too.
A regular way of coping with this battlefield stress and regaining unit morale was singing. Soldiers regularly sang songs in the rear areas, away from the actual trenches, that they generally made up themselves. These songs were usually quite cynical and comical. You may even find recordings of these songs in Music libraries today. Examples would be "Grandad's Army", and "Bawdy Barrack Room Ballads". Good singers were very valuable in rebuilding the shattered morale of men following a battle. Some songs, or versions of them, are still sung by some army units even today, during route marches.
I hope that is enough information for you, and good luck with your paper!
Good question! Have a star!