A Farm produces provisions by popping food type units (such as pigs). After a number of turns, the food type units will depop and related rations will appear in the larder of the nearest city and/or the capital.
Having a Warlord manage a city increases the yield of rations received from its attached farms.
Natural Allies do not need farms. Their allied side pops rations for them from its treasury. 
Farms are probably placed randomly like other Terrain Types, and thus make certain cities valuable because they are near the farms. Warchalking is described as though this is true.
Farms may require Units of the appropriate side to be present in them and/or working them. If so, this would allow claiming a farm using Units without building a nearby City.
Since barbarians and feral tribes do not have cities, they can acquire provisions from farms by harvesting food type units from them.
- ^ First Intermission 36
- ^ LIAB Text 4