The main conflict in Ordinary People is the death of Buck, the oldest boy in the Jarrett family. This event--a sailing accident caused by a storm on Lake Michigan--occurs one year prior to the beginning of the novel.
Conrad, the surviving son, attempted suicide six months after the accident due to an overwhelming sense of survivor's guilt, as he was the only other person in the sailboat with his brother at the time. When the novel opens, he has only recently been released from being an inpatient at a psychiatric hospital.
Beth, the mother, has pulled away from her living son and her husband, and attempts to cope with the tragedies (Buck's death and Conrad's suicide attempt) by keeping up appearances--hence the novel's title. She is a perfectionist to the point of obsession, and there is a distinct impression on the reader and on Conrad that she would have preferred that Buck survived the accident instead.
Calvin, the father, is simply trying to put his family back together, but is hindered by Conrad's deep depression and by Beth's extreme coldness. He finds it difficult to accept that he truly has no control over what happens to his family, or even what happens within that family.