1994 Ford Taurus SMOKING PROBLEM

Coolant system need to be checked
fill coolant and check for leak
pressure test will be best to do
check water pump
3.8 L engine check headgasket

Generally I have determined that black smoke is a sign of a rich fuel mixture.

That being said, it tells me that your engine is running far too hot for the car to handle with it's current (albeit limited) cooling capacity.

I think you have two-three problems here. One is the water isn't circulating properly throughout the system. Which could be a broken water pump, plugged radiator, and/or a kinked pipe. Also on older model vehicles, the engine gets rather clogged inside with rust, and sometime the freeze plugs need to be removed to clean things out, and flush your system.

I would generally have this system fully flushed, pressure test it, and refill with the proper 60/40 50/50 antifreeze to "Distilled" water mixture.
Don't buy the "Ready-made" antifreeze as your paying for water, and you need all the AF you can get, usually 2 bottles worth. A good flush chemical can help when you perform the flushing of the system.

2nd problem.
I'm assuming you haven't checked for trouble codes yet. Which would be the next logical step. You may have a Mass Air Flow sensor that is incorrect, a leaking fuel injector, and probably bad spark plugs and wires. Best to check the plugs yourself, and check the trouble codes on the car at any Autozone (they do it for free).

Fortunately, your not getting blue/white smoke, which would indicate to me, and I've been down this road before, that the cylinder head is cracked, and then life really gets miserable. I did a couple of cylinder heads, and they are no fun indeed.