All of the electronics (apart from the motors of course) go inside the box.
You will need the following components:
4 x Motor
1 x Propeller kit (2 times left and 2 times right rotating)
1 x Propeller accessory pack
4 x ESC (electronic speed controller)
1 x Radio receiver (with a minimum of four channels)
1 x Flight Controller
See the lest step of this instructable for the components I used.
Basically the circuit is something like this (see the image for a visual overview):
The battery plug connects to all of the ESCs. Each ESC is connected to a motor by its three thick wires. It's thin wires (power, ground and signal) go to the output pins on the flight controller. This provides the flight controller with power, and the ESC with a signal from the controller. Plug the ESC into the controller starting with the one connected to the left front motor, then the right front, right back and ending with the left back.
Depending on the actual hardware, it might be best to not have four power wires going to your flight controller (one from each ESC). It's better to be safe than sorry, so CUT ALL BUT ONE of the thin power wires from the ESCs (again, please see the image).
The radio receiver is connected to the input of the flightcontroller, which also provides the receiver with power. The way you have to plug it in might be different from controller to controller, so check your manual.
If your flight controller supports it, you can plug in an optional bluetooth module to connect to the controller without a cable. I would really advise getting a flight controller that supports this, because it lets you change the settings of the controller without having to open the box every time.
When you are done, put everything inside the box. Put the M3 nuts in the holes at the bottom of the box and put in the screws from the top. Be sure to check the front of the flight controller is pointing towards the direction you want to fly in, and when you close the lid, check if the arrow on top is also pointing in this direction.
At this point, you should be able to let your motors spin (make sure you don't attach any propellers!) to see if they are rotating in the right direction. The front left and back right motors have to move clockwise, the other two anti-clockwise (this is also indicated on the lid of the box). If a motor doesn't spin the right way, just switch any two of its three cables.
When I was done, I used some white wire wrap to keep the cables together.