The game is fragmental, without the introduction or the ending of the story or any explanation of what is happening. However, there is likely to be the story line relating the characters and the world they inhabit. Obviously, the story line is still being developed as the game is being expanded. The main sources revealing details about the story line are the promotional videos, hidden puzzles and the game itself.
For instance, Don't Starve Cinematic Trailer Forbidden Knowledge reveals how Wilson ended up in this world. For the puzzles see William Carter Puzzles topic. In the game Maxwell refers to other players and objects, for example, says that he kept Wes locked out since Wes is weak.
There are many nice details in the game, like how characters refer to objects which one could analyze and the infer about the story line.
Story development in the game Edit
The character is thrown into the world with presumably the game antagonist telling us "Say pal, you don't look so good. You better find something to eat before night comes!" and there are no other instructions. We learn about the world by exploring it and trying different things. As the game develops, one can come across the adventure mode during which the same antagonist will appear and address us again.
Summed up, the character explores the world which has loads of secrets and in the end, after completing five challenges in the adventure mode, confronts the antagonist. It looks as if the antagonist has designed some parts of the world but is not actually in control. Throughout the game we are haunted by shadow creatures which are holding the game antagonist and are likely to have cause the extinction of the ancient civilization.
Story development outside the game Edit
The game leaves many questions about the mechanics of the world and intentions of the characters. Some answers can be found from the cinematic trailers.
In one of the posts on Klei forums one of the developers outlined the structure of the story as they saw it at that time
1890s - 1906 Edit
William Carter origin story
William and Charlie enter the DS world.
1906 - 1910ish Edit
Some crazy stuff happens that we haven't told you about yet....
1910ish - 1921 Edit
The various playable characters get pulled into the DS world.
Wilson gets pulled in (Forbidden Knowlege trailer).
*THE ORIGINAL GAME + ROG STARTS HERE*
Wilson lives in DSworld for a while. Dies a lot, eventually finds Maxwell's door and confronts Maxwell
Wilson replaces Maxwell on the Nightmare Throne, Maxwell becomes Waxwell.
Charlie banishes Wilson back to the DS world and takes the throne for herself.
The DST plotline begins. Events of ANR occur concurrently.
The survivors (canonically Wilson, Wendy, Wickerbottom, and Webber, as seen in the ANR trailer) fight the Ancient Fuelweaver. Eventually, the Fuelweaver is taken away by Charlie. The Ancient Gateway destabilizes.
Winona arrives under (as of yet) unclear circumstances.
The events of The Forge event occur.
Wickerbottom activates the Gateway with the Ancient Key and six of the survivors (canonically Wilson, Willow, Wolfgang, Wendy, Wickerbottom, and Wigfrid) enter, transporting them to the Forge dimension. They battle a series of increasingly difficult enemies in Battlemaster Pugna's arena before defeating the Grand Forge Boarrior. Pugna surrenders and allows them to use the Gate to go back to their old realm, the Constant. Meanwhile, Charlie appears at the activated Gateway at the Constant end and draws a kind of energy out of it, though the exact nature of her interference remains unknown.
- William Carter arrives at Ellis Island from London, England on the 26th July, 1901. He is a tall, frail, nervous looking man with glasses and an accent, working as a magician and stage performer. He aims to stay with his brother, Jack, and family (including his twin nieces, Wendy and Abigail), but finds that they have moved out west to Corona, California.
- Without a place to stay and with an unpopular stage act, William struggles to stay afloat, and falls into debt for his show materials with a prop dealer named George T. Witherstone. Desperate and humiliated, he purchases a ticket to San Francisco by train.
- In August of 1904, the train strikes a broken-down circus wagon at the Old Mill Crossing. Many are injured, and Williams story is thought to end here, as he goes missing from the crash and disappears into the harsh Nevada desert.
- At some time during the events of that day, William resurfaces in possession of a strange book, the Codex Umbra. Using the knowledge contained therein, he reinvents himself as Maxwell the Great, a summoner of shadows. This new persona of his has much more confidence and stage presence and wears no glasses. He enjoys a substantial amount of success, although whether this is how he actually appears to others or merely how he views himself is a different question.
- Maxwell continues onwards to San Francisco (likely in the company of Wolfgang, Wes, and Wigfrids traveling circus), and sets up his show in the city. He puts out an ad for an assistant with "a curious demeanor and a keen interest in the mysteries of the universe" - qualities that match his own, but are in retrospect poor choices for the arts he now dabbles in. He hires a young woman named Charlie, and the two form a strong relationship in and out of their work.
- As he studies the book, Maxwell begins to see shadows and dark things forming unbidden. He still exerts a measure of control over his work, but as his work dabbles in the value of dark madness, he keeps it largely hidden. He remains in San Francisco, performing in his act and growing steadily more unstable and powerful in the occult, until April 17, 1906.
- On that evening, Charlie comes to Maxwell's apartment to check up on him and gather up the props for their show. She uncovers the secret passage to his study room and enters, attracting the attention of both Maxwell and a shadowy hand. As Maxwell intervenes quietly through a portrait to stave off the shadows, Charlie collects his things and reads the mad scrawls on his study room wall, visible only through the light of a special lantern. Making a hasty exit, she returns only to drop Maxwell a worried note, suggesting they take a break after the current run of shows.
- Maxwell meets Charlie at the theater that night and the two give one last performance. Reaching into the Codex Umbra to pull forth the shadows within, Maxwell instead finds himself pulled upon instead. He fights back, and shadows emerge from every direction, capturing both Charlie and Maxwell and drawing them into another world. The next morning, an earthquake levels parts of San Francisco, collapsing all evidence of Maxwell's existence and killing thousands.
- Charlie is consumed by the darkness. Maxwell is enthroned by shadows and trapped in the world of Don't Starve. He can create and manage parts of its existence. Much stuff happens here we don't know about yet.
- Overcome by boredom, Maxwell begins communicating with the outside world and drawing in new people, targeting stage performers and those who bear dark obsessions and secrets of their own. He lures them into the Don't Starve world and in doing so, traps them there.
- In 1919, Robert Wagstaff and the Voxola radio company release the Voxola PR-76, a revolutionary new radio and the thingy you see on top of the divining rod. Only a few are made before the factory burns down and Wagstaff disappears.
- In 1921, under urging by Maxwell through Wagstaffs radio, Wilson enters the Don't Starve world and the game officially begins. Like the other playable characters, he dies a lot. Canonically, he's the one who completes Adventure Mode.
- Wilson finds Maxwell's throne and frees his tortured spirit from the limbo he controls, crumbling his body to dust. Unfortunately, his rescuer is enthroned in his place, and Maxwell's spirit remains trapped within the world.
- This circle can only be repeated. It becomes clear that no one survivor can stop the true overlords of this world or achieve freedom from its clutches -- though perhaps many, sharing a common purpose, might battle the nightmares and win.
The information about the story developments surrounding the game have been gathered from this wiki and the below links