Gather carrots by looting villages, killing zombies, or trading with farmer villagers
Craft or find a hoe
Find or make a water source nearby
Use the hoe to till grass or dirt into farmland
Place carrots on the farmland
Keep the farmland hydrated by placing water within 4 blocks
Protect the crops from trampling by mobs or players
Wait for the carrots to grow through several stages
Use a bone meal if you want to speed up growth
Harvest the fully grown carrots
Replant some carrots to keep the farm going