If the refrigerator does not run at all and the light does not turn on when the door is opened, an electrical component may be broken, although it is worth resetting the circuit breaker first. If the light comes on, the problem may be with a cooling component.
Pulling the refrigerator forward and feeling around it can help diagnose the problem. If parts of the refrigerator are hot or cold, the mechanical components are partially working. Further diagnosis likely needs to be done by a professional, but the problem might lie with the refrigerant or the compressor.
If walls outside and inside the refrigerator remain at room temperature and the unit does not make any noise, the problem might lie with a fuse. Refrigerators have fuses to prevent power surges from damaging the system, and one that breaks can stop the unit from working. Replacement is generally simple. It is also worth checking the temperature setting to make sure the target temperature is not set too high.
Refrigerators rely on thermostats to determine when to run, and a broken thermostat can cause the system to stay off. Some thermostats have a reset switch, which might fix the problem. Most units also have a thermostat in the freezer compartment. If either is malfunctioning, the entire unit might not work.