The pull chain on my ceiling fan that turns the light on and off has come all the way out of the base of the fan. How can I fix this? I tried unscrewing the piece that the chain hung from, but saw no way to reattach a new pull chain.

You have to replace the switch assembly as well.

Here are instructions:

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

Before you start anything you have to turn off the fan... than you stand on a chair, than remove the chain from the fan.
Lastly you replace the switch.

Keke cute

Very easy. Just buy another swich and just hook it up the same way you take the other one out.