Sir Walter's mishandling of his family's finances is presented rather dramatically in the movie, with debt collectors arriving and removing things from the home before the rest of the family is made aware of the issue.
In the book, Anne's father is more direct about the matter and goes to his eldest daughter, Elizabeth, for advice on where costs can be cut.
Anne and Lady Russell are the ones who ultimately make a plan for refinancing the estate, with Anne playing a large part in making heavy cuts that Lady Russell originally kept in the budget.
Anne doesn't have any say on this in the movie, though she is in the room when Sir Walter discusses everything with Lady Russell and his lawyer, Mr. Shepherd.