Cables clean and tight on the battery? If so probably the starter solenoid. (Older F150s located just behind the battery on the passenger inner fender).
Does the engine turn over and then make the clicking noise while trying to start, or does it not do anything but make the clicking noise when you turn the key. If its not turning over at all then it might be a battery problem, Try cleaning the battery terminals, and/or charge the battery, Could also be the starter solenoid, but start with the battery first.
Maybe flat battery?
It could be solenoid, starter, battery, alternator not CHARGING the battery or corroded battery terminals.
Low battery voltage .?
More than likely the battery is to weak to start the engine. If it's not the battery, the starter may be the culprit.
A loud fast clicking noise is usually indicative of a low battery or a loose cable.
Probably it's a low battery, though it could be a bad starter. You are probably hearing the starter solenoid clicking.
dead battery or bad starter (with the clicking, I'm 95% sure its the battery)
charge the battery, change the battery, use the back up start either a pull start or kick start.
check your battery then the connections if it still wont start try changing the starter solenoid if possible
Dead battery? Maybe if it makes clicking noise -dead battery
Your battery is dead.