First, start nurturing the case study early in the process. Once your client has committed to purchase your product, start prepping them for the idea of being featured on your website and in your marketing materials. You don't have to mention being a part of case studies right off the bat, but let them know that when the project succeeds, you'd be interested in writing up the results.
At each phase of the project, involve the sales team at your company. Your sales rep should be following up at each step, making sure that the client is happy and documenting the client's successes. Once the project is successfully completed, the the client may not see immediate results. You can either do a case study right then while the project is still fresh if you want to focus on implementation, or you can wait until the client achieves ROI.
Either way, make sure the client knows what they're about to do and what's involved. Get clearance from the client's PR department and legal department to participate in the case study, then determine who the best person to interview is. For example, if you're trying to reach the director of analytics in your target market, have your case study writer interview the director of analytics at your client's location. Also have your case study writer send over preliminary questions. There may be follow-ups that your writer has to ask during the interview or interviews, but overall, your client will know what to expect during the interview.
But the most important thing to do is get approval and clearance from your client before you hire a writer. Otherwise, both you and the writer will be frustrated as your client jumps through corporate hoops to get the all-clear.