It can be quite the task to get to the bottom of things, especially if new to the company (process, acronyms, tools and systems names etc). Core questions are 'what are you trying to do', 'how do you do that', 'how can it be better' - identifying pains and gains along the way. Working on-site gives the luxury of future check-ins to refine the understanding. If it's complex and I can see them numerous times, I let people talk and build on it later, as too many questions can be disruptive and widen the scope of unknowns. I go away, map it, take it back and validate it, 2 or 3 times if need be. Better still, shadow them for a day.