The FAN on the air conditioner unit on top of my house stays running all the time.
The unit cools when it is supposed to, however when it's reached the room's temp, and the house thermostat automatically shuts of the unit, the fan staysd on. It even stays on when the slide switch on the thermostat is switched to "fan off".

Please tell me how to stop the fan running all the time. Thanks

Is this a self contained unit? If so it may be a bad blower relay. Try removing the cover from the thermostat and take loose the Green wire on the "g" terminal and see if that shuts it off.

Turn the fan to auto (automatic) instead of "ON" on the thermostat. My Mom (she is 80 years old) flips the switch and then nearly freezes before calling me. I go over and flip it back to "auto" and everything is back to normal until next time.