Minecraft wiki entry for Island_survival, associated text: Kelp is an easy initial source of food, which can usually be found offshore a short swim, and can be broken by hand. When broken deep down (leaving one block to continue growing) all the kelp above the breaking point breaks and floats to the surface. It is easy to harvest a lot of kelp quickly, and safe to do on the first day before threatened by hostile mobs. It must be smelted in a furnace first to get dried kelp. Dried kelp can, in turn, be used to craft dried kelp blocks, which function both as a substitute building block and furnace fuel.
Farming crops is a simple and easy source of renewable food. A farm can be created on any island. Look for tall grass and break it by hand, and you may get some seeds before exhausting the supply of tall grass, although bone meal can be used on regular grass to grow more tall grass.
Just one seed is enough to start a farm. Put a block of dirt level with the shore water up to 4 blocks from the shore, craft a wooden hoe and use it on the dirt to turn it into farmland, and plant the seeds. Wait for them to mature before harvesting the wheat, which also yields more seeds, allowing for expansion of the farm. Three wheat can be crafted into bread, which is a good food source.
With a farm, you can grow wheat, carrots, potatoes, beetroot, and other crops. Some crops can be used to breed animals, if animals are available to breed.
Fishing with a fishing rod is the best way to get high-saturation foods once you have two string from killing spiders. Crafting a fishing rod gives an infinite supply of good food, and it is usually renewable as damaged enchanted fishing rods are often fished up.
While fish may be eaten raw, they are most nourishing when cooked. You need 8 cobblestones for a furnace as well as fuel (wood logs, or logs smelted into charcoal, which is the more efficient fuel) to cook the fish. An alternative option is to make a campfire, which requires no fuel apart from the charcoal or coal used to craft it and cooks four pieces at a time.
Swimming after fish to kill them with a weapon or pickaxe risks being attacked by drowned. On the other hand, killing a fish this way can also drop a bone, which can be crafted into bone meal for speeding up the growth of crops and trees.
Apples occasionally drop from oak leaves (1⁄200 drop chance) when broken or decayed. Of course, this requires the island to have an oak tree.
Carrots and potatoes are also rare drops from zombies, but not available early in-game. These can also be found from shipwreck chests later in the game.
Rotten flesh is a last-resort when all else has failed. Wait until zombies spawn at night and kill them, or wait until morning when they burn in sunlight to get rotten flesh.