How to Survive Minecraft on Hardcore Mode

Search the trees nearby and begin collecting wood from it. As soon as you have 3 logs, bring up your inventory screen and craft them into wooden planks. 4 planks should be used for crafting table, 2 for stick.

Place the crafting table somewhere close to you, right-click it and create a wooden axe. Mine the crafting table with the axe so you can store it back into your inventory again. From there, continue collecting wood with the newly crafted axe you made.

2 logs should be enough, only use 1 out of the 2 logs you collected for wooden planks. You should still have enough sticks laying around for one more tool, so use those to make a wooden pickaxe. Get at least enough cobblestone for a furnace and some stone tools (If you happen to see coal somewhere, mine it with the pickaxe). Decide where you are going to carve your small temporary home into for the night. The three recommended options are underground, mountain, or a tiny island.

Your home should be small, you don't want to spend too long on something that isn't a permanent shelter. Place your crafting table somewhere inside your home and make a furnace. If you have not got any coal as of yet, you may want to make charcoal. Luckily you still had not used that one other log you collected. Smelt the log with wood planks or sticks, and when it's finished, grab the charcoal from the furnace and make torches. Place it all around your shelter, block up the entrance with dirt, stone, or whatever. Now you're set for the night (No wooden doors for the entrance, since zombies can break them easily).

If you still have enough time, go out and collect more wood (more sticks and planks), stone (upgrade all your tools to stone), and coal (more torches). You may also slay animals for meat and cook it in the furnace. You could also make a chest to store unnecessary items. Do all of this until nighttime has arrived.

Check frequently from time to time to see if the night had ended (alternatively, you may leave one block open so you don't have to do this, however, it's a little risky). Next, you're going to want to craft a stone sword and have torches, cooked food, and other stone tools. You may encounter creepers, spiders, and endermen, so get your stone sword ready to slay them (Zombies and Skeletons won't be burned by sunlight if hiding under a tree or in the water).

Look around for tall grass, destroy it to get seeds to grow wheat farms. This is important especially when all the animals in your area are no longer there. Find an ocean or a lake, use a stone hoe to turn dirt or grass into farm land around water. This way, the soil will become hydrated by the water flowing into it to make wheat plants grow faster. Place seeds into the farm land and a few torches (If you do not have any, then this would be a good time to get plenty of them). It may take a while for the wheat to grow, but keep on planting and planting so it makes much more of an impact when it's fully grown.

Go out on a journey to find sheep. You need their wool to make a bed, so slay three of them. Sleep in the bed when it's nighttime, skipping to daytime without monsters spawning would make hardcore a whole lot easier.

You may want to think about a tree farm as well, just to prepare, destroy leaf blocks for a chance of a sapling dropping from it. Plant it anywhere where there's dirt, room, and light. Add one torch or so to make it grow even when the sun isn't out. You probably don't need to do this now, but maybe later when you're running out of trees.