Your first order of business will be to arm yourself.
You can find rocks by digging in dirt. Keep some of them to use as ranged weapons, and throw the others at the ground (by right-clicking) to break them into flint. You can combine two flint to create a flint toolhead.
You can find sticks in the dirt, too, but you’re more likely to find them by breaking leaf blocks.
Finally, you can find plant fibers by breaking tall grass. Four fibers can be combined into a cord.
Once you have a toolhead, a stick and a cord, you can make yourself a flint knife.
You’ll also want to find some food. Your best early options come from trees. Oak and dark oak leaf blocks can drop acorns, and spruce leaf blocks can drop pinecones, in which you can find pine nuts. If you’re in a plains biome, you might be lucky enough to find an apple tree. Those drop apples on the ground, so you can collect food without breaking anything!
Now you’re ready to do some hunting. Why hunt? Because you’ll need leather in order to make tools. On the plus side, pigs and sheep now have a chance to drop leather, so you don’t necessarily have to find cows, horses or rabbits. On the minus side, passive mobs won’t just stand around waiting for you to hit them. You’ll have to chase them, or pelt them with rocks from a distance.
If you absolutely can’t find any animals, as a last resort, you can kill zombies, which will sometimes drop patchwork flesh from which leather can be made. But you really shouldn’t be taking on zombies yet.
Once you have leather, you can use your knife on it to create leather strips. And once you have leather strips, you can combine a toolhead, a stick and a leather strip to create a flint hatchet.
Hurray! You can finally chop down trees, which means you can finally construct a crafting table and make other tools, such as a flint pickaxe, a flint shovel, and a flint hoe. You’re ready to start mining and farming!
There are two more things I should mention here. First, bows are now constructed with leather strips rather than with string. And second — and probably more importantly — while your flint pickaxe will let you mine stone and coal, it will NOT let you mine iron. For that you’ll need “bone-encrusted stone” tools.
“Bone-encrusted stone” tools are made with rocks, bone shards, sticks and leather strips. Bone shards can be made by carving bones with your knife. But don’t worry. You don’t necessarily have to fight skeletons to get bones. Lots of creatures have bones, after all, so lots of creatures now have a chance to drop them.
Finally, you’ll probably spend more than a day in the game before you can actually mine any coal and make “real” torches. “Primitive” torches won’t last long, but will at least last a night. Make a simple woven cloth with four cords, use your knife to crush some seeds for oil, and make a “bow drill” from two sticks and a cord. Combine those three items with an extra stick, and you’ve got light!