The cornerstone of any successful farm, and of doing well at Hay Day in general, is to plant and grow as many crops as you can. Putting heaps of seeds in the ground isn't enough to make money, however. First off, though, you have to purchase a 'Patch of Dirt', upon which you can dig and plant seeds. These cost just 1 Coin from the Shop. You are limited to the amount of patches of dirt you can buy, to stop people from just spamming seeds. More are available to unlock as you progress.
Once you have harvested a plant, you can then process it, if you wish, for something worth even more Coins. Wheat and Corn results in Chicken Feed, for example. This works the same way that you can process Milk, produced by any Cows that you may have on your farm, to make Cheese.
You begin the game with three farm plots. Later on in the game, as you rise through the levels, you will be able to unlock more plots - generally this occurs by three more plots per level. You can purchase more plots in the Store under the Fields option in the first tab.
Tap on one of the empty farm plots and you are able to choose which crop you would like to plant. To plant, tap on the seed icon that you would like to grow, then drag it onto the plot in question. The seeds will then begin to grow! Each Field will produce two crops.
Farming is the main source of income in Hay Day
The fact that each Field rewards you with 2 crops means that you potentially get one to replant, and one to sell or use.
To plant new Fields, open the Shop menu. You will find Fields at the very top of the first tab. You will unlock three new Field plots at Level 3, which will be the first opportunity you have to plant more. Each Field only takes up one square of land, so you have to work quite hard to get a significant return on each one.
The game will warn you if you are about to use up the last of a particular crop. The reason you don't want to do this is obviously because you then won't be able to replant it - instead you would have to use Diamonds or buy it from another player.