The Lone Wolf scenario is unlocked with 100 experiences.
These can be collected by playing any of the other scenarios. You'll likely gain a decent understanding of the game while doing so, so I am going to skip basic gameplay in favour of just telling you what the new items and mechanics are and what the best way is to survive.

Lone Wolf has two gamemodes, Crescent Moon and Full Moon. The latter needs to be unlocked separately for 50 experiences, gives you Bloodlust which allows you to eat raw meat for experiences, and makes wolves more common and aggressive. This guide will focus on Crescent Moon, as Full Moon is very similar and just offers you an easier way to get experiences in exchange for more danger.

Lone Wolf puts you in the shoes of a person who has fled into the wilderness to survive the lovecraftian apocalypse that seems to have driven humanity to the brink of extinction. The titular Lone Wolf has been alone for some time, and will reveal small hints about their backstory when reaching important milestones, like building effigies or killing your first wolf.

There are also interesting monologues given under specific circumstances, like meeting your first wolf, making it to the first night, or finding buildings or campfires. To me, these monologues are the most interesting part of the scenario: They are well-written, help ground you in the setting, and can be surprisingly emotional (the effigy flavour text in particular).

It is worth noting that experiences are hard to get in this gamemode, so it is not recommended to use Lone Wolf for grinding purposes. Try playing DotW as madman for that.

There are about a dozen items unique to this scenario that you will be able to find or make. The basic set consists of berries, mushrooms, saplings and twigs, these are used to get access to a larger array of crafted items.

Berries can be harvested (~5 turns) from blue-coloured berry bushes, which are common throughout the forest. They will be your main source of food and connect to a longer chain:
(1) On their own, they can be eaten, and will move you from Starving to Hungry.
(2) If you have three berries, you can craft a rabbit snare. These will provide you with a rabbit carcass after some time. Rabbit carcasses can be cooked and will remove Starving or Hungry, but will not give you Satiated.
(3) Rabbit meat can be poisoned with mushrooms and used to lure wolves. Killing and butchering a wolf will yield a wolf heart, wolf meat and a wolf skin. The heart can be eaten, and lowers your sanity while giving one of your stats a permanent boost. The wolf-meat can be cooked for a Satiating meal, and the wolf's skin can be worn as clothing: It decays over time, but will make other wolves more reluctant to attack.

Mushrooms will occasionally spawn in the woods and can be picked up in one turn.
They are poisonous, and eating them does not restore your hunger. While the poison from mushrooms will drain your health (not enough to kill you unless you're already wounded), it will also regenerate your sanity.
Their main use is to poison meat, as a way to hurt and weaken wolves. You can poison rabbit meat by equipping it and then using the 'poison meat' function on the mushroom. When poisoned, wolves will run away, giving you a relatively safe opening to pelt them with spears until they die.

Saplings are small trees that usually stand by themselves in clearings (Not adjacent to other trees). They can be harvested (>15 minutes) and then converted into Spears (~30 minutes). Spears can be used as melee weapons but also thrown or used to build pit traps. Spears can be sharpened, lowering their durability but doubling their damage. The durability will drop significantly, and may break the spear. Sharpening can drain anywhere from 0 to 11% of duability, so it's smart to collect as many as possible; If you're lucky, you'll be able to get a 200 or 400 damage spear with enough durability for a few attacks. Having several sharpened spears will be necessary to effectively hunt and kill poisoned wolves, as well.

Twigs spawn around the forest. If you have three, you can make an effigy. When placed, the effigy will restore 25 sanity and serve as a landmark. As such, making effigies is a reliable and efficient way to restore your sanity without any side effects.

The roaming wolves are your main obstacle to survival in this scenario, and are still a major threat even when you've gathered enough supplies to try hunting one: If a second one shows up, that's your sign to run away.

Wolves are generally aggressive in Lone Wolf. A single one may sometimes disengage or keep its distance, but you should assume one will give chase if it sees you. In this case, your best bet is to throw a stone at it to try and stun it, or to wrap around some trees or walk through bushes. Killing a wolf is difficult. Barring the lucky find of a gun and two or three rounds of ammo, or an explosive in one of the buildings, attacking them head on is a death sentence, as they are capable of draining your health in two or three attacks and have a high health pool (400).

For this reason, it's important to collect stones and have a decent supply of them at the ready. Thrown stones have a decent chance of stunning an enemy, which leaves them inactive for three or so turns: Hopefully enough to make enough distance to get behind a tree to break line of sight.

Wolf behaviour is a more complex than that of most other enemies, and they will react to certain conditions. Your Sixth Sense allows you to read the "Thoughts" of nearby wolves, which is especially useful when there's one closeby that you haven't seen yet. All blurbs:

Scent of man: The wolf is close, but has not seen you.
Sight of man: The wolf has seen you and will likely chase you.
Scent of blood: Triggered when you are bleeding.
Scent of meat: Triggered when you are carrying (rabbit) meat.
Fire: Wolves will keep their distance from bonfires. Being close to a lit one will provide you with safety, and if you back away from the wolf, it will probably be unable to chase you because the bonfire is in the way. Wolves also keep their distance from wildfires.
Death: Wearing a wolfskin will trigger this message from wolves. It makes them more reluctant to attack and chase you, but can be overriden if you are carrying meat.
Hungry: This message appears from the second day onward: Wolves will be more desperate and eager to attack.
Kill: This message will appear when a wolf is chasing you and very close. At this point, you're either preparing to take it down in one or two turns, or you're about to die.

On the third day, a red cannibal wolf will spawn, differentiated from the other wolves by having its letter appear a crimson red. This wolf will be *much* more aggressive and seem virtually impossible to shake. By the time it spawns, you should be ready to kill it: Either save up explosives or firearms, or have traps and throwing spears at the ready.
The Red Wolf will ignore rabbit meat. I am not sure whether it is drawn to wolf meat.

The map in Lone Wolf is mostly a lot of forest with a handful of buildings spread around.
-There are 4 small, hard-to-find cabins across the map with a handful of loot items each. You spawn in one which can have between 0 and 3 items.
-There is a single larger, central building that can be found besides the railroad tracks that bisect the forest. This building reliably spawns a decent (>6) amount of loot items. If you're very lucky, you can get your hands on a gun and some matching ammo, or materials for a pipe bomb or gas grenade.
-In addition, there are countless campsites with two to three minor loot items and an unlit bonfire. These bonfires can be kindled and will provide somewhere between thirty to sixty minutes of fire without needing to provide firewood.

Here is a map provided on the DitW fanwiki by user Melonchu.

The short answer is you'll probably die anyway. It can take a long time to find your way to enough loot spots to actually start crafting and working toward setting traps, and odds are you'll run into a wolf at some point without being in a good position to escape. In addition, getting unlucky with your starting items (or getting no items at all) can make your run significantly harder.

However, even if you were to start with no loot, there are still ways to get ahead in the scenario, and we all know that DotW isn't about surviving but about doing things before you die.

For self defense, it's a good idea to gather up stones. When equipped, these can be thrown at wolves. This won't do a meaningful amount of damage to them, but has a decent chance of inflicting stun, which will either buy you some time to run away, or allow you to prepare for combat (not recommended unless you're prepared).

Bonfires are the most reliable way to keep wolves at a distance: They will not come close enough to attack if you have one lit. Setting up a bonfire takes time, so it is best to prepare an unlit fire if you're planning on foraging in the area, and running back to it if a wolf spots you. Because of this, it is also safe to read or craft next to a bonfire, as long as it burns for long enough to finish your task.

There is no need to prioritize finding buildings. In fact, the best way to survive is to go slow and play as a nomad. Calmly gather up forest items and prepare a bonfire with enough firewood to last a good 4 or 5 hours. Leave saplings, mushrooms, firewood and twigs at your bonfire while collecting items in the area, and work toward crafting a handful of rabbit snares, have these set up in a ring around your campfire by the time it's fully dark.
Once it's dark enough for Dread to kick in, light your fire and focus on crafting: Spears, boiled water, snares and effigies should be your priority. Reading books or crafting bombs, shivs or other items you can create with what you've scavenged should also be done at this point. It is not wise to roam around once it's fully dark, because wolves will be more aggressive and you will be unable to see them or any loot you'd want to collect.
If your rabbit snares go off, be sure to collect the carcasses to butcher and prepare them. Eating rabbit meat should only be done if you're desperate: It is more useful to poison it and use it as bait to hunt wolves.

Hunting wolves is the crux of this gamemode: Leaving meat for them will distract them and keep them in one place for several turns. If the meat is poisoned, it will start draining health once the wolf is done eating it. While it eats, you should pelt it with spears (it is also viable to walk up to it and attack it in melee). Once it is done eating, it will most likely start running away. Chase it and stay close; It will likely die of poisoning, at which point you should equip the wolf carcass, butcher, cook and eat is as soon as possible.

Red Wolf
The endgame for this scenario is the Red Wolf which automatically spawns on the third day, or has a very low chance of spawning in place of a normal wolf. This wolf will be much more persistent in chasing you and likely has more health, as well. Killing it will be a challenge, so saving up ammunition or explosives to kill it should be a priority.

This mode doesn't really have a larger-scope story like the default scenario does, and there's no collectable notes. Instead, your character will monologue about themselves and the things you encounter when specific conditions are met. I have decided to include all lore, including the one only found by completing the game mode. Beware of spoilers.

First wolf sighted
The wolf.
I see it, and it sees me, and there is an understanding there.
I am an intruder here, in this untamed world.
I am he who bites without teeth, I am the claw outside bone, I am the weak god to these animals.
I am a competing predator.
They plague me, these wolves.
I know when they are coming.
A hush passes through the woods.
Mice, rabbits, and even the other horrors that stalk the world since its fall, all silent.
All silent but for the soundless voice of the wolves.
Long have I cowered from them, but no more.
They know I can't fight them, not when they have greater weapons than I, when they gather into packs and become aggressive.
But I am a human being.
And we did not steal this world from nature by submitting to its fangs.

Finding a campfire
An old fire, gone cold and dusty.
I could rekindle it for transient warmth and safety.
But I cannot rely on it- to be still is to court death.
Am I alone, here?
Did I make this fire, or was it someone else, wandering these woods?
I wonder, if they saw me, would they just see another abomination?
Another man-eating creature, feasting on the rotting world.
We are so very small.
If there was someone else, we could wander forever among the trees, and never meet one another.

Entering a building
The wolves know to steer clear of buildings.
They smell of mankind’s age of power, and entering them means claustrophobia, entrapment, starvation in a senseless, sharp-angled place.
Human construction is as incomprehensible to the animals as the stars are to us.
We take from nature, and something new, something catered to our needs is born.
For the things beyond humanity, I wonder, does the same principle apply?
Has something essential been stolen, to raise edifices we cannot understand?

Making an effigy
I have made an effigy in the shape of a man.
How odd, it is, to look at it and see myself.
I don’t feel human.
I hardly speak anymore, even to myself.
My thoughts blur into abstract concepts, complexity slipping like fat cut from bone.
I forget my family, what they looked like, how they sound, how they smelled, how they felt, how– my stomach churns.
Looking into the straw face, the featureless, expressionless face, a strange thing in my throat flexes.
And I speak.

Hello.

Crafting a snare
One cannot live on rabbits alone.
Their bodies are too lean; you'd have plenty of food, but your body would run out of the stuff it needs to break it down.
You'd starve while stuffing your face.
I must show restraint, not gluttony.
I will place rabbit traps far apart, lest the struggling of one rabbit warn others to stay away.
Nature has a strange way of balancing itself.
In order to truly feast, predator must eat predator, risk life and limb.
I wonder sometimes why the wolves do not turn on each other.
There is plenty of meat right there, why hunt me?
I receive no true answer.
Just the accusing stare of their animal eyes.

Getting rabbit meat
Meat is the first and last currency of monsters.
It all came from the same ultimate source, that first cell that decided to divide and cling together.
It became flesh, became bone, became blood.
Then, divided further, ate pieces of the world, and brought them back to the whole.
Ate itself, recursively, forever, expanding.
Humanity forgot this, once upon a time.
Forgot that we were monsters.
When the end came, and humanity was no longer the dominant monster, we were panicked.
Some hoarded dead meat, to pay for their lives.
I alone knew that only living meat could sustain me.
Thus, I alone survived.
Even those that stalk me follow this absolute law of flesh.
With this bloody coin, I can bribe my hunger away, or buy my life from the jaws of the wolves.

Making it to day 2
The sun sets, and the howling begins.
At night, the wolves rule the woods.
They see darkness like daylight, and if they catch me, they will kill me.
The cabin is my only place of true safety.
At humanity's dawn, wolves were our enemies.
But there was a respect there, too.
We took wolves, and twisted them with kindness and breeding into mankind's only friend.
They guarded our herds, guarded our homes at night.
Perfectly loyal, like we made them.
It seems only fitting, that at humanity's dusk, wolves would become our enemies once again.

Killing your first wolf
The wolf's blood paints the soil.
I've killed it.
I've KILLED IT!

I imagine myself the wolf.
Eaten by blood frenzy, ripping apart the corpse before me.
Such bounty. Such strength, brought low by my hand!
I will take it into myself.

Days of horror come back to me.
Meat of a different kind.
I drown the guilt in hot wolf blood.

I can wear its skin.
The other wolves will see me, they will smell the blood and decay and hatred on the wind, and they will fear me for the first time.

Making it to day 4
A hunger builds in me. A hatred.
Is this to be my life?
I chose to be alone, to save myself from the world's crumbling.
And now I fight for each scrap of food, each hour of life.
Always the wolves, hunting me.
I see their yellow eyes in the darkness, accusing me.

No, wolves do not eat their own.
They are so proud of that, so proud that in their tiny feral lives, they have never been so desperate. No more.

There is one among them, a wolf with bloodsoaked hide.
He alone does not accuse me, only hungers for my meat.
He is the leader of the pack, the head of this dragon.
I will cut it off.

(SPOILER WARNING) Killing the red wolf
The beast slumps to the ground.
Blood stains its fur further, stains my mind and vision red.
A rush of euphoria overtakes me, and I scream to the heavens.
A keening, a howl, it burns my throat.
This human animal I've become has vanquished its rival.

There is a flash of sadness for the one creature left who, perhaps, understood me.
Perhaps it did not hoard its family, as I did.
But when pushed to the brink, it fed all the same.

I could skin the red one, in full view of its brethren.
They can't stop me.
I know they would strike only out of jealousy, craving a share of the meat.
I can still hear them.
Their simple madness, their innocent bloodlust that is vital to their being enters my mind.

Where does the hair end and the fur begin?
Where does the man end and the wolf begin?
Which is sharper, the canine fangs or my own shattered grin, or my own unnatural teeth and claws that I build from everything I touch?

There are myths of the man who becomes a wolf, but those mean nothing to me.
I am the wolf who becomes a man.
I bend the world to wolven will, I make monuments to my own survival.
I shed my past, my humanity, and make right all my misdeeds.

A wolf has no morality to transgress against.
A wolf has only a pack.
A wolf has only territory.
And these woods are mine.