The answer to 'ceiling fan outlet not working' is that there are several common causes, including a tripped circuit breaker, a faulty wall switch, or a problem with the wiring. Symptoms may include the fan not turning on at all or the light not working even when the fan is running.
To troubleshoot, first check the circuit breaker to make sure it hasn't tripped. If the breaker is fine, use a voltage tester to check for power at the ceiling fan outlet. If there's no power, the issue is likely with the wiring or a faulty outlet. At this point, it's best to call an electrician, as troubleshooting and repairing electrical issues can be dangerous for DIYers. If the outlet has power but the fan still doesn't work, the problem may be with the fan itself, which you could try replacing or repairing yourself if you're comfortable working with electrical components.