When you first turn off the engine the water (coolant) temperature actually goes up because the engine is still hot, and the coolant is not flowing through the system to cool it down. Your radiator may actually boil over for a few minutes, which is why all modern cars have a coolant recovery system (overflow bottle) installed. Check the hose going from the top of the radiator to the coolant recovery bottle. A small pin-hole in that hose could spray a fine mist of coolant all over the fan belts and engine. And check your radiator too, to be certain it is full up to the top when the engine is cold.

Check both your upper and lower radiator hose, lower hose is usually under the car on drivers side and upper is on passenger side. If you noticed your upper radiator hose collapses you have a bad pressure cap but if your car does not over heat and run normal temp you might just have bad hoses and spend 30 buck and put on new hoses, if that doesn't fix the problem get it looked at, it's probably an internal problem

First of all, if you are in the United States then the passenger side of the vehicle is the right side. Always. And you should probably take your car to a mechanic and get it looked at. You could need something as simple as a hose, or it could be something more involved. You really should have a professional look at it.

What do you expect to learn here? Are you a mechanic? I must presume no. Therefore, since coolant can leak from many, many locations in an engine, only a mechanic can resolve this issue. Most people take their cars to a mechanic for repairs. I suggest you do that.

If it is leaking only when the car is off. Residual pressure that builds up when the water is not circulating and hot puts pressure on the pump seal which is bad and causes the leak. If you don;t fix it soon the seal will fail altogether

I drive a 1993 Chevy Lumina APV. And recently i've started to leak coolant from the left side (passenger side) of the vehicle. It leaks only when the car engine has been shut off. Sometimes I see fluid on the drive belt which I just replaced. I was leaking coolant before I replaced the drive belt. I have a feeling that this is my water pumps way of telling me its dying, but i guess Im just looking for other ideas. It's hard to determine if its leaking from any hoses because to be honest, most of t the stuff down there is a damp from the leakage. Any ideas?