Actually the smoking / cancer link is very hard to really prove. How can you conclusively link an act (smoking a cigarette) to its consequence (getting cancer) when the two are separated by perhaps 40 years of possibly related health events?
Smoking / cancer is proved by careful statistical analysis of very large studies. Or rather, you repeatedly do large studies, narrowing confidence intervals each time, until you reach a point where things seem to tip over in people's minds from "unproven" to "proven".
It's really very like climate change in many ways.