Rust guide: Surviving your first day
Let's go crafting!
Collect as many resources as possible until hunger or darkness sets in, then craft a wooden shelter and place it in an out-of-the-way corner by putting it in a quick-access slot and then selecting it. Craft and attach a door the same way, then go inside, lock up, and make a campfire. Place and start it, then press and hold the "Interact" key and click "Open" when the menu pops up. Put the raw meat you collected from your kills—it will all be chicken breasts, by the way—into the "Cook" square and give it a few minutes to roast up into a tasty meal. Meat won't go bad, so cook as much as you can.
With the food on the grill, go back into the crafting menu and whip up a bow and a bunch of arrows—20 or 30 at least. You'll need 35 wood and five cloth to make the bow, which is why you may need to kill multiple animals with your hatchet. The bow isn't terribly accurate but it hits hard and makes hunting a relative breeze, and at this stage that's what you need.
If you have sufficient cloth remaining, make armor; if not, whip up what you can, then eat up (at least some of the chicken should be cooked by now) and go hunting. Depending on how much was left over after building the bow you're going to need 40 to 50 pieces of cloth to make the next big jump in progress, so don't be shy about killing everything you see. Once you have enough, get back home and craft whatever armor remains unmade plus a sleeping bag.
Place the sleeping bag on the floor of your cabin to create a respawn point, then build a wooden storage box, place it and put excess food, wood, stones, and whatever else you can spare inside. Having a stocked-up respawn point makes bouncing back from death a lot easier—assuming nobody comes along and blows it up.
Gearing up and getting serious
By now you should have a good supply of basic crafting materials, so at this point the game becomes less about staying alive and more about transitioning from prey to predator. Use animal fat and excess cloth to make low-grade fuel, then use that and some rocks to make a furnace. Wood, metal, and sulfur ore goes into the furnace; charcoal, sulfur, and metal fragments come out.
Use wood and stones to make a workbench—it'll be crowded in your little hut but everything will fit as long as you're not too sloppy with the layout—and with all the necessary furnishings in place you can craft a proper firearm, plus gunpowder and ammunition.
It's a lot to do in a single day but with a good jump on the morning and a little bit of luck, it won't be much trouble at all. And now, properly armed and armored, you're ready to strike out into the world. But keep the bow—bullets are scarce. Good luck!