As the man on the radio said, you have two ways of escaping. Either by building a ladder or by repairing the car. In both cases you will need to find a hammer and then break the glass from the red box on the wall to obtain the the Emergency Door key.
The box with the Emergency Door Key can spawn on any wall.
It's a good idea to start checking the walls for it soon as you start the game.

Escape doors are on the 1st floor.
To escape with the ladder you will need 3 planks, a saw and a rope.
Use the workshop table to cut the 3 planks with the saw (it will generate a lot of noise) and then make a ladder using the rope.
Then go to the 1st floor, unlock one of the doors with the Emergency Door Key and use your ladder on the wall.

Escape door is on the ground floor, under one of the staircases.
To escape with the car, you will need a tire, tire wrench, car keys and motor oil.

After unlocking the exit door, you will have to get the car ready.

You use the motor oil to fill up the car.
Then you use the tire wrench to put the tire back.

Last thing is to just use the car key and run over the monster :)

To open the stuck door, you need to cut the wires from the fuse next to the door by using a cutter.