Characters and information

I read Cryptonomicon probably ten years ago. An excellent novel. One I obviously still think about. It ends with a system for encoding information. The Moon Is a Harsh Mistress, if I remember correctly, includes in its narrative instructions for creating spy networks. What information might one of your characters teach another (and perhaps incidentally the reader)? How might that “teaching moment” characterize the teacher and the student? How informally could it happen?