The Farmer is the backbone of your food production. The Farmer will cultivate the crops you assign it through the Field block (a scarecrow).
Before the Farmer can start, you need to craft the Field block. Place the Field block in the plot of land you want the Farmer to work on and right-click on it to access its GUI. Here you will place the crop you want for this specific field to be cultivated. The crops the Farmer will currently cultivate are wheat, carrots, potatoes, beets, melons, pumpkins, and most crops from other mods as long as they have normal growth behavior. (Sugarcane and cactus are produced by the Planter.)