Farming is done through the use of Plots. You start out with 9 plots and you get more from the Crafting Menu with each level upgrade.
Planting and Harvesting
To plant a Crop you tap on a plot, which brings up the Crop Menu. From here you can choose the seeds you want to plant and drag the crop to the plots you want to seed. Crops go through three stages, Seeds, Sprout, Flowering and Ripe.
A Ripe plant is ready to be harvested, which is done by clicking on its plot. A Scythe tool will appear, which you can drag across all ripe plants in one motion. If a Ripe crop is left too long without getting harvested, it will rot. You will have to clear the rotted plant the same way you'd harvest it in order to plant something new.
For each crop you sow you get two back when you harvest. Not a bad deal!
Also, note the diagonal Farm View, where the camera shifts to better show your actions. When you re in Farm View, your Avatar doesn't move, although you're free to do all the farm tasks you need, as well as pan the camera across the Farm's expanse.