What are the causes for the windshield wiper fluid to stop working?

Possibly multiple causes:

Easiest fix: the reservoir is empty, or the fluid is frozen iin the tank or in the lines.

Slightly harder fix: the fuse for the pump is blown or the tube that connects the pump to the nozzles is broken/disconnected.

A little more difficult fix: switch or pump is broken.

After you put the key in, go to accessory, turn off the stereo, heater, and anything else that makes noise and depress the button for the wiper fluid; if you hear a humming sound the pump is working. If it's frozen, replace the fluid with a good low temperature version.