We usually start with quick overall impressions, then go around with a few prompts: "what's something new you learned?", "what didn't you like?", and "what didn't you fully understand?" (every paper has something, whether it's the evaluation methodology or some algorithm detail). That last question tends to drive most of the discussion because people chime in and build on each other's answers. Sometimes you get lucky with domain expertise in the room. For example, when we read "What Every Programmer Should Know About Memory"[1], one of the attendees was a former Intel engineer who spent their career in memory systems. They answered questions the rest of us wouldn't have even known to ask.
How exactly are the meetings structured? I.e is someone leading discussions? Does each person go around and share thoughts? Etc