Joseph springs the trap he has set for his brothers in this chapter. The Bible doesn't explain his motivation, but it's not hard to imagine several possible goals.
One might be testing their care for their youngest sibling. When Benjamin's life is on the line, will they leave him to suffer or will they rescue him? Judah chooses to offer himself up in his brother's place, to take the punishment for him. The analogy isn't perfect, since Benjamin wasn't guilty and Judah wasn’t without sin, but it foreshadows Christ's stepping down from heaven to take our place.
Another motivation may have been for Joseph to protect Benjamin from his brothers. Perhaps Joseph worried about his older brothers mistreating the youngest son, especially when they spoke of how their father doted on him as the only remaining son of Rachel. Would his brothers treat Benjamin as they had Joseph?
What about the reference to divination? Was Joseph really using the silver cup for a pagan fortune-telling ritual? Or did he mention that as part of his Egyptian disguise to heighten the importance of the stolen cup? The example of foretelling given (learning that his brothers had the money and cup) was clearly not the result of divination, since he directed his servant to place the money and cup in their bags, there's no evidence that Joseph practiced divination.
What does this teach me about God? That He loves us and seeks to restore broken relationships.
What does it teach us about people/ourselves? Even when we haven't committed a particular sin (stealing the cup), the penalty for sin still exists, and we need someone to take that penalty for us in order to restore our relationships with one another. Jesus did just that.
How will this impact my life this week? What if I looked for opportunities to be that peace-maker? Not just keeping the peace between parties divided, but bearing the consequences for something I didn't do in order to foster peace and reconciliation.
What about today? Lord, help me to be mindful of how generously you've forgiven me and be quick and generous in forgiving others. (Starting with the drive in to work!)