Your Prediction Model works. What to do after?
You could do the following:


Find out the most important predictors used by your model; the methods used to identify importance depend on the model used.
For each of the major pedictors try to find out how does each predictor segment the customer population of will-churn vs. will-not-churn. That would be the starting point for framing hypothesis of why these set of customers are churning. Generate reports/info-graphics showing how these predictors impact the tendency to churn. Sometimes predictors are not causes but side-effects of the hidden cause showing up elsewhere. So be open to skepticism about the predictors.
Involve the business/users and have brainstorming sessions to go through each of these hypothesis and evolve the most practical and economic actions that could be taken to reduce churn. Before you get into a discussion, plan for a sufficient amount of time, come up with your best thought actions which you feel will address the situation and have all the details gleaned from your analysis available for sharing in the session.


This is an art more than a science and your ability to understand the domain as well as good communication will help you achieve this goal.