Using farms you can grow plants. After researching crop rotation you can start farming multiple plants in a single farm. Crops need water to survive, and can be fertilized to improve the fertility threshold, which determines the amount of units you will receive from the crop. In most cases ordering of the plants in the "growth calendar" does not matter, as long as the two plants next to each other are different, as having two identical plants farmed after each other will result in growth penalty. Growing the same plant in the first and last "growth calendar" counts as the crops being grown after each other therefore it adds the growth penalty.
Fertilizer does not seem to provide any changes from the mechanical perspective. The added benefit is higher crop yields, with high fertility need crops like Soy Beans benefiting more from fertilizer than low fertility need crops like potatoes. In summary, the more fertilizer, the more crop yields, although as you get closer to the maximum fertility, the smaller the benefit you get. Still, even at maximum fertility the diminishing returns are rather negligible.
Given that you can specify up to 4 types of plants to be farmed on a single farm, there are many combinations which a player can reach, and below you can find a few of them. For the sake of consistency, we consider Green Manure to be a plant as well, but not a crop.
Farm with 1 plant
Initially farms can grow only a single plant, and later on the player can keep farming a single plant on a farm if they wish to. However, after researching the the crop rotation, if the player wishes to improve the average yield of any crop, it is always beneficial to add in a single Green Manure plant.
Farm with 2 plants
As mentioned, farming 1 crop with Green Manure always returns a better average yield, than farming a single crop. However, if the player wishes to maximize the average crop yield, growing two crops of different kind results in both plants having a highest yield possible when combined. Meaning that if you have two farms, and you decide to grow Potatoes + Vegetables in both farms, your final yield of both crops will be higher than if you grew Potatoes + Green Manure in one farm, and Vegetables + Green Manure in the other.
Farm with 3 plants
Having two plants of the same type adds a penalty, therefore it is optimal to grow 3 plants of different kinds. Having Green Manure as one of them does not make a noticeable difference in the final crop yields, therefore having 3 different crops is better. However, if you remove one of the crops, and place it into another farm, you can get higher yields by adding another crop or Green Manure.
Farm with 4 plants
They work, but you can always split them into two farms, which always give you higher yields.