While it may not necessarily feel true for a lot of people, most people have some specific role they fill which, if it were to be filled by someone else, would require a certain amount of instruction. Fictional characters, be they from a story or game, almost all have roles like this; after all, designing characters who do one’s-not-sure-what, even if their narrative roles are clear, can make for more bodies floating around than anyone actually wants. As a result, pretty much all of them should have some spot that actually would be empty if they left it.
So, for this exercise, take one of your characters, and consider a role that that character definitely fits. Now imagine that she’s going somewhere—on vacation, on a possible suicide mission, undercover, whatever—and she’s chosen someone to cover for her and take care of her duties within her squad/organization/government/household/whatever until she gets back. (Figuring out who it is that she’s chosen might make for a more interesting result, but it’s strictly optional.) Got that? Good. Now, what sort of last-minute debriefing would she give her substitute? Think both about how she’d give it—note, phone call, personal meeting—what sorts of things she’s instructing the substitute on how to do, what sort of tone she’s using, and whether there’s anything she’s doing to make especially sure that what needs to be done gets done (and, if you feel like it, any of her role she’s still insisting on carrying with her.)
The fun thing about this one is just how much you have to actually think about, or if you’re the kind of person who just slips into voice and emerges twenty minutes later with a full riff, how much you can learn from it. It tells you what the character thinks her role is, and what importance she assigns to it; what skills and traits she thinks are necessary to get it done, and which ones she assumes her replacement should already have; what processes she takes for granted, and which she thinks require particular instruction—and that’s not getting into how these are colored if you know exactly who the replacement is, or know of the specific reason why the character is being temporarily replaced.
Note also that these don’t have to be particularly important things, just things that the character considers herself responsible for. Instructions for taking care of a house can give you just as much information as instructions on keeping a country out of trouble or making sure an adventuring group has its proper arcane backup; it’s all in how you look at things!