Page Revised: 10 May 2019
So you're late for work. You dash out the door, jump into the old Cougar, put the key in the ignition, give it the old twist...and you get a lovely clicking noise where the sound of the car starting should be. Power drainage, right? Not necessarily.
Fords generally need just about 100 percent voltage for ignition. Any power drop or bad connections and it won't start, period. After ensuring the battery voltage is at least 12.2v, the first thing to check is your battery connection. If there is any hint of corrosion around the terminals that's usually the problem. Sometimes you can't even see any gunk but it'll still cause the same problem. A terminal cleaner should be mandatory in any Ford owner's toolbox; that'll keep them clean and prevent this problem from occurring again. Also it's highly recommended that you keep the terminals protected from any future corrosion. Those red and green felt washers they sell everywhere really do a great job. Or you can use terminal cleaner or even grease. If your battery is not maintenance-free, make sure it has enough water (always use distilled or reverse-osmosis water when filling, not regular tap water).
The next step in the line would be the starter solenoid, located by the strut tower nearest the battery. If you happen to overtighten one of the nuts on the terminals, chances are you can break the contact internally, and you'll get intermittent or no starting. This also happens over time naturally. Fortunately, solenoids are very inexpensive and it should be very readily available for your car/engine bay. It never hurts to have a spare laying around anyway.
If you happen to have a 1983-84 vehicle you have a Duraspark II ignition system. Bruce has provided a link to help troubleshoot this system, along with some diagrams and vital information.
Lastly, if a solenoid swap-out doesn't solve the issue then you could have a power drain, bad battery, bad voltage regulator, bad alternator, bad ignition switch, bad TFI module, bad starter motor, etc. But at least these tips will not you cost much to eliminate some possible causes.