After getting the initial premise, you need to break it into smaller pieces in order to understand what is required. Each piece will raise different questions that you will ask your customers later. These questions will help fill in the gaps for your POC, ensuring that your questions cover all business needs from all view standpoints: the business standpoint, the functional standpoint, and, finally, the technical standpoint. One good way to keep track of the questions that arise and which business need they will be resolving is to have a checklist that asks which standpoint the question is being asked from and what is resolved or answered.
It is also important to note that, as questions become answers, they can also come with constraints or other obstacles that will also need to be addressed and mentioned during the POC stage...