For a good guide, see our main article on farming in Minecraft. To convert land for farming, you'll need to till the dirt and irrigate it with a source of water.
Modernization gave us hybridization — cross breeding. From carrots, lettuce, radishes and other fine seeded species to the larger seeds of beans, pumpkins and tomatoes, every gardener kept a stash of their favorites to plant again or trade with friends. Like in real life, carrots have seeds to plant in order to grow more carrots. It just makes sense. Carrot seeds should be added and it should be added in the 1.14 update with the villagers. This is the same way that carrots are planted in the game. You can't just plant a carrot in the ground and more will grow. Unlike wheat, you don't need a special seed to grow potato crops — you plant the raw potato itself.