Find carrots in village farm plots
Break carrot crops and collect the drops
Loot carrots from chests in village houses, shipwrecks, or other generated structures
Kill zombies, husks, or zombie villagers for a chance to drop carrots
Trade with farmer villagers for carrots
Use a carrot on a stick only after you already have a carrot
Grow your own carrots by planting one on farmland and harvesting the mature crop