Not a stupid question at all. The films touch upon it, but don't get into it in much detail.

You get part of the story from the discussion between Vito, Sonny & Tom just prior to the Sollozzo meeting. IIRC, Tom mentions that they're already into labor racketeering, gambling, and prostitution, I believe. (In Godfather II, Roth mentioned that he & Vito had been running rum together during Prohibition, so there's also that.) And then of course, at the big meeting with all the Mob chiefs, Vito reluctantly agreed to provide legal, political & financial support for the narcotics trade as well.

As Michael began to transition the family to Nevada, the family retained a presence in both gambling and prostitution - but in Nevada it was legal gambling (casinos) and legal prostitution (brothels) - and expanded into the hotel business, and I believe, the entertainment business as well.

I'm sure someone much more knowledgeable about these things than me can elaborate further...