I'm afraid there are too many conflicts in this book to really do this question justice in anything less than many pages. We can, however, get you started on answering this.

There are conflicts between Susie and her neighbor, Mr. Harvey. This is resolved when she's killed.

After that, the major conflict in the book is between Susie's death and the rest of reality (seriously). She is in conflict with the universe, because she's trying to figure out the meaning of her death. This is mostly resolved through her sister finding love, and through her making love with Ray in the body of another woman.

Her family tries to make sense of her death, and this creates a host of related conflicts. Her father and mother end up in conflict with one another. This takes years to resolve, and her mother has to leave and come home again.

Her little brother is so hurt by her death that he ends up with psychic defenses that last the novel.

The police and Susie's father are in conflict; this lasts most of the book.

Grandma Lynn's energy and personality clash with the family's loss and mourning.

Ruth Connors' encounter with Susie gives her insight into violence, especially violence against women, and she spends the novel trying to resolve this.

Detective Len Fenerman is in conflict with Mr. Harvey, with Susie's family, and with himself, due to the affair.

You'll find quotations related to each starting here:
http://www.enotes.com/lovely-bones/preface-chapter-1-5