The majority of the episode is a dream sequence, in which the actual Christmas Carol segment takes place.
-Beavis is the equivalent of Ebenezer Scrooge, depicted as at manager of Burger World. -Principal McVicker is an employee working under Beavis, who has a large, poor family he can barely afford to feed. He is the equivalent of Bob Cratchit from the original story, with his family being the equivalent of the Cratchit family from the story (although it is worth noting that no member of his family is a "Tiny Tim" style character.) -Butt-Head is Jacob Marley, Scrooge's old business partner. -Tom Anderson is the Ghost of Christmas Past.
-David Van Drissen (the boys' teacher) is the Ghost of Christmas Present.
-Coach Buzzcut is the Ghost of Christmas Future.
As the segment is only about 15 minutes long, naturally not all of the elements of the Christmas Carol story can be touched upon. For instance, Beavis is not revealed to have had any past love interest or anything like that.
The ending is optimistic, but not in the same sense as the original story. In the original story, Scrooge has an awakening and knows that he can change into a good man. In this episode, Beavis awakens from the dream happy, but he is only optimistic because in the future, he will have his own VCR and pornography to watch in it, meaning he completely missed the points the Ghosts were trying to make, further parodying the original story.