You've got a few things you have to get figured out first. To begin with, you need to make sure the compressor isn't seized. Loosen the belts a little and put a ratchet on the center bolt. It should have some resistance but still turn. If so, good!
Next, the wire in the top picture is the compressor clutch wire. Without that hooked up the clutch will never engage under the pulley to run the compressor. It is connected in series to the low pressure cut off switch at the receiver/drier canister above the right front fender. If you can't find a matching connector, it probably got cut off. Try tracing the wiring harness to see if you can find the point where it was cut. Otherwise, you'll have to run a new wire and splice it into one side of the switch. The other wire on the switch connects directly to the push button switches on the dash.
When you've got all that wired up you can try to see if the compressor will run. With the engine running, try pushing one of the a/c buttons to see if the compressor kicks in. Most likely it won't. In fact, it would be very surprising if it did work. Chances are the refrigerant is low or gone from the system. An a/c system that old is bound to have leaks, probably several, and will require repairs. Without refrigerant, there is no pressure and the switch at the canister will stay off. Also, the oil for the compressor is carried by the refigerant and without it the compressor will seize in no time. The switch really is there to protect the compressor.
Try jumping the low pressure cut off switch. Pull off the rubber boot with the two wires in it and stick a jumper wire between the connectors. If the compressor starts running, you know you got the wiring right, so the pressure must be low in the system. Warning: only run the compressor for a few seconds at a time...it doesn't have oil going to it, remember!
If it still won't run, re-check the wiring. You can try to run a jumper wire from the connector at the compressor that is in your top picture to the positve side of the battery. If it runs, you have a problem in the rest of the wiring. Remember, only run it a few seconds at a time! But, if it still won't run, you've got a bad clutch coil and it will have to be replaced.
If the refrigerant is low, then you have to make some choices. Either have a mechanic repair it, or try it yourself. You also need to decide if you want to use R12 or R134a or some blend of R134a. Don't think you can just go to Walmart and get a can or two of whatever they have and put it in. First, you said a kid had the car and heaven knows what he might have put in it and it might not be compatable. Also, the old oils and seals used in R12 systems won't work with R134a. And, if it has a leak, anything you put in will leak out too and you're just throwing good money after bad.
If you do it yourself with some work you can convert to R134a. But, you will need to buy, rent, borrow, or steal the following tools: an a/c manifold gauge set, a vacuum pump, a refrigerant can valve, fitting adaptors, and valve core tool.
The best thing to do right now is see if you get the compressor running and come back and discuss what is the best next step.