Can you tell me how cancer causing agents usually lead to cancer?

Mutate genes: A few of them caused greatly increased cell turnover instead which is the fertile soil in which mutations caused by other agents can be expressed. Remembering that all true cancers are mutagens is a good way to tell which "things that cause cancer" in media / pop reports are probably true (radiation, smoking, mutagenic chemicals) and which ones are bogus / statistical flukes / scare talk.