When a car has black smoke from exhaust this indicates that there is too much gas that is being burned. Therefore, to solve the problem we must know why the car burned too much gas?
The usual cause of having problem of black smoke from exhaust is a clogged air filter. Since it is the usual cause then it's the part to look first. Locate the air filter and examine if the air filter has a lot of dirt. If so, then it is more likely that causes the problem. When the air filter is clogged this will prevent some air from reaching the engine combustion chambers thus causing the air/fuel ratio to become rich, meaning the amount of fuel is too much compared to the amount of air entering the combustion chambers. When the air filter has a lot of dirt, just by replacing the filter will solve the problem.
Another possibilities is a vacuum leak, a vacuum that is created on your car fuel system is the one that determines how much fuel the will get. When there is a vacuum leak the air /fuel ratio will is possible to become too rich making the combustion chambers to burn some excess gas causing the black smoke that comes out the exhaust. However, if there is black smoke from exhaust when accelerating then the problem is a bad valve stem seals. To determine if your car has vacuum leak, locate the hose connecting to PCV valve and check if there is crack.