Find carrots in villages, shipwrecks, or from zombie drops
Equip the carrot in your hotbar
Till grass or dirt with a hoe to make farmland
Place the carrot on the farmland
Make sure the farmland stays hydrated with water nearby
Keep the area lit so the carrots can grow at night
Wait for the carrots to mature
Harvest the fully grown carrots by breaking the crop
Replant some carrots to keep growing more