the older spare tire carrier wasn't a very good design, i removed mine a long time ago and keep the tire in the bed. it's essentially a "T" shape with one bar going side to side, bolted to the frame on both sides, and another bar going from the center of the first bar to the rear of the truck. that bar is hinged on the first bar, and bolts to a bracket at the rear of the truck. the idea is that you detach the end from the bracket at the rear, then pivot the tire down. it's a little cumbersome to load up the tire and store it away, plus a trailer hitch will get in the way of the hardware at the rear of the truck.
i guess ford had a spare tire carrier that put the tire in the bed on the drivers side, standing up at the front corner of the bed. it was used on trucks that had dual fuel tanks, but ive never seen one myself. oversize tires don't really fit there, but for smaller tires, i think its a much better option than the other style.