By "field" do you mean the field of crops? The field can be an object in your game (for example, a TiledBackground, visible or invisible), or it can be a logical identifier, like an instance variable on crops sprites. Every game is different and it's up to you to decide how you make it.
Functions, groups, families, hierarchies, containers are not mandatory for a game like this, but they will make the job much-much easier. I highly recommend you study how to use these features.
For example, I would probably combine all crop sprites into a family. When planting crops, add them as children to the Field object. This way you will be able to easily pick crops growing on each field, and perform some generic actions (like watering) on the entire Crops family.