Quite a few people help Jess to cope with the death of Leslie. I think the person that has the biggest part is his father. Throughout the novel, it's clear that Jess's dad isn't the most tender, caring person in the world. He and Jess are not incredibly close, but after Leslie's death that begins to change.
The first way that Jess's dad helps is by driving after him when Jess runs out of the house. Dad drives after him and picks him up and carries him back. This is a very loving image. Dad understands what his son is going through and wraps Jess up and attempts to comfort him by being a strong physical protective presence.
Mr. Aarons does try to talk to Jess soon after Leslie's death, but Jess isn't willing to listen . . . yet. Out of anger, Jess throws the paint set that Leslie bought him into the river. Dad again goes out to his son and tries to talk to him. This time, Jess does seek out his father's thoughts about Leslie and the afterlife. Mr. Aarons does a fantastic job of comforting Jess like a young boy (by holding him) and talking to him like a young man (the discussion of heaven and hell).
Mr. Burke is also comforting to Jess. Jess goes over to the Burke household after the death and Mr. Burke hugs Jess and thanks Jess over and over again for being such a great friend to Leslie. Mr. Burke also gives Jess Leslie's pet dog. He wants Jess to take care of the dog while they are away. The dog helps bring Jess some comfort.
The last person that really helps Jess cope is his teacher, Mrs. Myers. She expresses her sympathy toward Jess and tells him about the death of her husband and how that made her feel. It comforts Jess to know that there is someone else who knows exactly how he is feeling.