Louise Erdrich's Love Medicine, offers a diverse group of stories and characters. It is, perhaps, what makes her novel so worth reading: it describes the complexity of the human condition, interrelationships, and insights into the reservation life of Native Americans, specifically the Chippewa.
Trying to imagine what might be selected for a final test on this novel is difficult because it is a collection of stories with related (literally) characters, but there is no continuous plot line, and there is no traditional timeline. Traditionally, when reading a novel we can concentrate on main characters and significant aspects of plot development and conflict resolution, but it is very different for this book.
For my recommendations, though this is in no way written in stone, I would concentrate first on "The World's Greatest Fisherman," as it is the first story which introduces a wide variety of characters and the inter-workings of their relationships, as well as some sense to the culture.
Personally, I especially liked the stories "Saint Marie," "Wild Geese," and "The Island." "Saint Marie" is a little creepy, but a fascinating take on good vs. evil. "Wild Geese" seems a continuation of "Saint Marie," but from Nector's viewpoint. (And some of his questions for Marie we can only know the answers to having read the previous chapter.) "The Island" steps completely out of a short sense of timeline to introduce Lulu, who we will "visit" throughout the book.
I would make sure to study "The Red Convertible," as this is a highly anthologized short story. "Love Medicine," I would think, is a must, as the concept of "love medicine," introduced in "The Island" is discussed in more detail here; core Chippewa beliefs are present; and, this is the chapter for which the book is named.
While it is important to have read and reviewed the entire book, I would doubt a college professor would concentrate on especially minor aspects of the novel as much as he/she might on central ideas and characterizations (different than a high school teacher). With this is mind, I would think it prudent to make sure to also be familiar with the final two chapters as well.
I'm not sure if your edition of the book has it (maybe they all do), but if so, I would study the family tree at the beginning of the novel. It may help to see how all these characters are connected, especially because their stories follow no chronology.