The chain no longer works to turn on/off the light. I would like to know how to take apart the fan & repair the problem.

The ceiling fan light switch is easy. Switch usually available at a hardware or ceiling fan store.
Crimp connectors may be used by the OEM. Wirenuts can be used on the replacement. It's an SPST pull chain switch with only two wires.

Ceiling fan pull chain replacement and repair - Ceiling Fans N More

I have found some three wire fan,light switches. To replace the switch , Remove the lights, under bottom cup like cover { three small screws to remove} then pull off cover and remove old swith { before cutting draw out on paper how the switch is hooked up} Replace switch ,replace cover ,replace lights. { DO ONE THING FIRST< TURN OFF WALL SWITCH OR THE BREAKER IN HOUSE POWWER PANEL} Hope I was OF help: