I've played for several hours now, eventually I found Maxwell's Door, I know that at the end of the five levels mentioned you unlock Maxwell, the thing is, I've no idea what to do inside these levels, I failed to go through the first one since I have no clue on what to do and 'cause I've little or no resources I eventually die.
When you first enter Maxwell's door you will start in a random world. Nearby you will find the divining rod and some basic supplies depending on the chapter theme.
To move on to the next world you have to find all four pieces of the wooden thing and piece it together. The divining rod will give out a sound depending on your distance to a piece.
It's hard to survive and move on to the next chapter, but if you fail you will continue in sandbox mode and can try again.
The objective is to assemble the Teleportato.
This is done by finding the five Things- the Ring Thing, the Metal Potato Thing, the Box Thing, the Crank Thing, and the Wooden Thing. The first four are items which must be used on the Wooden Thing to assemble the Teleportato.
The Divining Rod which you receive at the start will help- it detects how close you are to the nearest Thing.
This will transport you and a limited number of items to the next level of adventure mode. Complete enough levels and
After completing five levels you will confront Maxwell himself and be able to defeat him.
The objective is to survive, gather all four pieces of the Wooden Thing, assemble it, and activate it in order to progress to the next chapter, through 5 chapters plus an epilogue.
Each chapter has various features that make it more difficult than Sandbox mode.
The wiki has all the details.