All we know about the circumstances of Paul's death is that he was killed on the front lines on an otherwise quiet day. His death was not part of a big battle or heroic action. Since the book is mostly told from Paul's point of view while he was alive, we do not have his own account of his death. Like everyone else it seems, we have to rely on the official military report that simply states "all quiet on the Western Front." At least we can assume that Paul died relatively quickly and without too much agony from the statement that follows which says that "his face had an expression of calm, as though almost glad the end had come."
Although the book does not describe how Paul died, the 1930 cinematic version of All Quiet on the Western Front does attempt to fill in the blanks. In the film, Paul is shot dead by a French sniper as he calmly and carelessly reaches out of his trench in an attempt to touch a butterfly.