Once you have two flint, you can make a tool. Go ahead and start out by creating a Pickaxe.
The pickaxe can be used as an improvised weapon but It's mainly used towards mining Boulders and various other rock constructs.
Once boulders and such are mined, materials will explode out for you to pick up.
What you especially want to be at the lookout for is Manure and Beefalos. "Poop" is essential in creating a stable source of food income from farming. So pick it up whenever you see a bunch.
Beefalos can also be killed for a whole bunch of meat but they are rather difficult to kill and should instead preferrably be kept alive for manure alone.
Now that It's starting to get dark, you should create a campfire. To achieve this, you need some wooden logs so create an Axe using twigs and flint.
Equip the axe by rightclicking on it then chop down a tree.
Preferrably, we want to create a Fire Pit, due to higher efficiency with firewood, but unfortunately I didn't get enough stone due to no nearby boulders so a normal campfire will have to do.
Making a campfire is absolutely essential at night, as monsters come out to kill you the moment you're not near a lightsource.
Once It's night, don't wander off or you'll die. Stay near the campfire and make sure It has plenty enough fuel. If it starts to burn out, throw more materials into it, preferrably pinecones or logs.
Once It's day, continue to explore and gather as much food as possible.
In this case, I got quite lucky with my run and located a pack of Beefalos to achieve a whole bunch of manure with no effort.
"Close by, I got even more lucky and found a small Pond. Ponds spawn frogs that can be killed for Froglegs (which can be cooked for food) and they can also be fished out of, given you have a fishing pole.
And as luck would have it, I found a spider nest just south of the pond.
As you go into the "Sticky area" around the big egg/base, Spiders will pop out and charge you. They are rather easy to defeat as they get stunned from any attacks you do but let them group up too much and you'll be in trouble.
In this case, I took minimal damage because I created a Wheat Vest out of all the grass and could successfully kill all the spiders.
Destroying the base afterwards is also recommended as It drops more silk + disables hostile spiders to come chasing you at night.
"Locating some Pig Houses is also a good idea as the name implies, they house pigs. Pigs are also a rather essential mob to have as you can feed them fruit & veggies to produce manure while also making them become friendly towards you, being on your side in times of battle.
Harvest some more manure before you explore onwards.
You may also come across various weird things in the world of Don't Starve such as these Worm Holes that bring you to random locations on the map. They are generally best avoided.
Pressing (TAB) will open the ingame map. It's extremely useful for seeing what you have explored and what you haven't.
If you're really lucky, you may even come across some randomly generated loot piles of previous adventurers.
I urge you to continue exploring until you find one of these Quarry Biomes. They are VERY rich in boulders which will be essential to progressing in the game.
Get your first, glorious Gold Nugget and craft a Science Machine to unlock a whole bunch more recipes.
New recipes will first have to be made with "Prototypes" before you can make them away from the machine. If you make a Prototype, you'll gain 15+ Sanity. Something highly useful to know.
A priority is to create a base at this point. Chop down some wood, make some wooden planks at the Science Machine in the Refinery tab and then create a chest.
In chests, you can dump all the stuff you don't need and not have to worry about ther items disappearing or being otherwise stolen.
If at a quarry, you should break no sweat finally crafting a fuel-efficient Fire Pit.
These are worth their weight in gold as they allow you to spend more time doing important things other than constantly chop trees down for firewood.