How do I attach this product:
to the back of my Ford F-150?
If your truck already has a receiver for a hitch, that puppy will slide right in, and a great big cotter pin holds it in place (or you can get a locking hitch pin so nobody steals it).
If it doesn’t, you can get one installed at most garages and shops. Bigger U-Haul places will do it for you as well.
And the partner needs to be the female receiver for this hitch. Since you are asking this question, you mus not have one. The end you have is the cheapest one. Females are always more expensive.
Look at the piece protruding from this thing:
http://www.autoanything.com/GenericPages/ProductImage.aspx?GroupID=undefined&ImageID=66369&ProductID=3874
Does your truck already have one of those sticking out the back? If it does, your hitch will slide right in as the Wombat explained. If not, you have to buy one of these kits first.
My truck has nothing like that. So how does that thing attach?
It gets bolted to the underside of the truck. They are make/model/year specific, so get one made specifically for the year of your Ford F150. You can then install it yourself or have a shop to it. Once that is installed, any of the standard ball hitches (like you linked to in the OP) will slide right in.
One thing, though, is that you will also need to install the wiring for the trailer lights. A truck with a factory installed trailer hitch will have a wiring receptacle next to the receiving end of the hitch. But if you vehicle doesn’t have that, you will need to purchase and install a wiring harness as well.
[QUOTE=jtgain]
My truck has nothing like that. So how does that thing attach?
[/QUOTE]
Usually, very easily. Hitch receivers these days are built specifically to a given make and model, and (usually) bolt on using existing drilled and tapped holes in the frame. Certainly DIY-friendly. Now, if you need to add wiring for trailer lights and brakes, that can get challenging, but an F-150 probably has the wiring already in place.
Something like this:
http://www.etrailer.com/Custom-Fit-Vehicle-Wiring/Tow-Ready/118242.html
I have a wiring receptacle. And a simple hole in at the base of the tailgate below the license plate.
It is a simple install for this “female” receptacle or do I need a pro?
See the whole problem was that the trailer hitch had to ride too high (with the attached ball above the hole in front of the license plate). And I had two of them. With the product in the OP, I can haul both trailers at the proper level (below the tailgate level).
It’s a 2003 Ford F-150. I’m usually pretty handy with this stuff and have a couple of weeks to do some handy work. If I can order and install, then I could save some cash. If it will kill me or set the truck on fire, then I will contact my brother in law. 
I installed my own hitch and wiring on my Ford E-150 Club Wagon many years back.
As mentioned, there were already holes in the frame for it to bolt onto. There was already a connector in the tail light circuit that unplugged. I had a purchased harness that plugged in providing the required electrical connections. If you need electric brakes it gets more complicated.
You’ll need a torque wrench to tighten the bolts attaching the hitch.
Highlighting mine
Isn’t this always the case? 
Don’t worry, the truck will catch fire all by itself.
(Former owner of a Ford F-150 and victim of the “Ford fires”, and who will NEVER again own a vehicle that is associated with Ford.)
Are you trying to get the hitch ball higher, or lower than mounting it directly onto the bumper in that hole?
If you’re trying to make it lower, and you have already been towing it with just a ball on your bumper, then you should be able to get away with one of these much cheaper female ends. They will install directly to the bumper. And if you were able to install the ball onto the bumper, this won’t be any more difficult than that was.
There are also some lowering adapters available. Check here:
http://www.bageco.com/hitchlistbump.htm
And here’s the plug in connector if you need it.
Good site Bear_Nenno, I’d forgotten all about those devices.
Beautiful. Just what I was looking for. Many thanks, guys.
Now that you’ve got that receiver installed, and you’re not towing a trailer, you’ll need to keep people away from that fancy truck.
I’ve got just the thingyou need!
Love it! Debating whether I should purchase it right now! Keep picturing the shit-storm it might cause on base, though.