You said your son ran it dry - of coolant? As in the radiator was dry or really low on antifreeze or dry as in no oil? If he ran it out of antifreeze and it caused the car to overheat and you're seeing water leaking underneath I would think that's what caused the overheating in the first place. Aka, something has a leak or a hose failed causing the car to overheat rather than him overheating the car causing a leak. Your leak would be the source of the issue.
It should be easy to spot if it's leaking while the car's not even running, that's a good sized coolant leak. Follow the drips, use a flashlight and look up under the car. Check around where you see it dripping from, even if you see coolant dripping from the bottom of the radiator it may be leaking up higher like from a hose. Check hoses, wipe them dry with a shop rag or paper towel and run your hands over them feeling for fresh coolant. Don't forget to check hose clamps.
It would be normal for it to leak faster when you start the car since you're putting the cooling system under pressure with the water pump running. If it's not leaking fast enough to find the source easily when the car is off, rather than starting it (and potentially being under the car while it's running) try removing the radiator cap.
Where it's leaking can give a general idea of what it might be. If it's near the front, check hoses, radiator, around the drive belts along the face of the motor (where the water pump is). If it's leaking closer to the passenger compartment (toward the middle of the car) it could be heater hoses or an intake manifold running down the back of the motor.
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