It is never explained how Arnold Friend knows so much about Connie and her family. When he confronts her at her house, he is able to tell her exactly where her family is at that moment: a picnic. He also knows that Connie's mother is helping to husk corn and that her older sister, June, is wearing a blue dress. It is possible that Arnold has been stalking Connie and procured his knowledge of where her family was going and even what June was wearing that day through spying on the house, but this would not explain how he knows exact details such as what the mother is doing at the picnic from afar.
One of the more popular interpretations of Arnold Friend's ability is that it is supernatural in origin. In critical discourse, Arnold is sometimes linked to the devil himself, a figure of pure evil seeking to tempt and destroy his victims. His grotesque appearance is often made a factor in these arguments: his skin is almost translucent, he appears to be wearing a wig, and he wobbles on his feet when he walks, almost losing his balance when giving Connie a mock bow, suggesting he's hiding hooves, a traditional element of medieval depictions of the devil. Ultimately, these interpretations are all the reader can go on, because otherwise, the author gives no explicit reason for Arnold having such intimate knowledge of Connie's life.