NSAIDs (non-steroidal anti-inflammatory drugs) for cluster headache work primarily by inhibiting cyclooxygenase (COX) enzymes, which reduces prostaglandin synthesis and subsequently decreases inflammatory responses and pain signaling. While they can provide some symptomatic relief, their effectiveness in cluster headache is limited compared to other treatment strategies like triptans or oxygen therapy, and they are generally considered a secondary or adjunctive treatment option.