The refrigerator furniture doesn’t do anything. The minifridge is a vehicle component; it has to be mounted onto a frame. You can mount it to a vehicle if you have one, or you can get a frame of any sort and deploy it (the frame) through the construction menu (*) with the Start Vehicle Construction option. You will need either a wrench, or a welder and welding goggles to mount the fridge (I can’t remember which).
The minifridge can be engaged through vehicle controls, meaning that if you are setting one up in your base you will need to install a vehicle controls to actually turn it on.
The controls do not need to be installed exactly where the minifridge is, but they must be on the same “vehicle” as the minifridge is.
Once it’s mounted you will need a power source (Car Battery, Storage Battery, or the like) mounted on an attached frame to power it. Without a power source the minifridge won’t do anything anyway. Be warned that it will consume power at an immense rate, so a Storage Battery is best.