Penelope "Punky" Brewster is an abandoned 8-year-old who wanders into an empty apartment in Chicago. The manager of the building is a 60-year-old curmudgeon named Henry Warnimont, who begrudgingly agrees to let her sleep on his couch until more suitable arrangements can be made.
In the first segment, Mrs. Johnson finds the task of walking the children to school to be too exasperating, so she turns it over to Henry, who attempts to instill a sense of discipline into them. In the second segment, Henry tries to introduce Punky and her friends to the joys of fishing.
In the first segment, Henry gives Punky a lucky nickel to keep with her while she goes for a booster shot. In the second segment, Punky can't sleep, so Henry agrees to let her stay up and watch the opera with him on TV.
By playing Santa at school and saying he can do anything if she believes in him hard enough, Henry has inadvertently convinced Punky that Santa Claus will bring back her mother. Now he must find the woman, but the search is fruitless until an antiques dealer provides a possible clue.