Each Family starts with $10,000 which they invest in a number of ways: buying up clubs and brothels, bribing officials, running drugs rackets. The aim is to thrive, to make money and control territory. The game could go on indefinitely, but the winner is the most powerful Family when play stops (because people get bored/need to do other things/agree a time limit).
Each Civilian starts with $500. Their aim is to set up a successful business and make more money than the other Civilians. They too can buy properties on the map (though not illegal ones). The only realistic way to protect those properties is to engage mafia help, and to set up in an area where the mafia is friendly.
The playing area is divided into four parts. There are three Family homes, where the Families can hold secret counsel. Then there is the communal City area, where the Civilians set up their shops. Any players can interact in the City area.
Your strength is measured by the territory you own, as much as by the money in you coffers. The game is played on a map of New York divided in to the five counties (Manhattan, Queens, Bronx, Brooklyn and Staten Island) and subdivided into neighbourhoods. You control a neighbourhood if you own a property (e.g. a speakeasy) in that neighbourhood or if it is surrounded by neighbourhoods on which you own a property. Each neighbourhood can only support one Family-owned institution.
If you are a civilian you may buy one property per neighbourhood regardless of mafia presence. Unlike the mafia, you don't automatically get rights to land adjacent to your properties.
Here is a copy of the map.