This is an exercise I did with a writing group. It is especially useful when trying to work through difficulties with characterization. In the writing group, we were each having trouble understanding the nuances of our main characters - basically, why our main characters weren't "cooperating." In this prompt, your main character is away for an extended period of time, perhaps at summer camp, or at grandma's house. Or maybe he's away at boot camp for incorrigible youth. In your letter, describe the problem you are having with him (the scene in question, stilted dialog, unrealistic motivations, whatever the problem may be) and ask your main character why this problem exists between the two of you. Try to understand and make connections between how you feel, act and think, to your characters strengths, differences, challenges and core values.
When you have written your letter, read it out loud. How will your character feel when he reads this letter? What emotions will come to the surface? Can he find a way to cooperate with you, the writer? Or is there something about his basic character that will make it impossible for him to do what you think he should be doing? Is there anything you should change as a result?