Correlation provides a starting point to investigate causality. To establish causality what you do is develop hypothesis for mechanisms of causality, identify intermediate events that may be observable if the mechanism hypothesis is valid and observe for those events. If these are observed, you have a much higher likelihood of causality. You'll typically do this if the return on investment from establishing causality is high enough since it's much more work - eg. You're trying to get a drug approval from FDA or you're trying to justify a major investment decision.