If the smoke is gray or black in color, it typically means the vehicle is running rich (too much gasoline and not enough air). If you only experience this when the car is started, it is typically an issue with the settings of the fuel injection system. If you get black smoke all the time, there are additional problems with the fuel injection system that needs to be checked (oxygen sensors, map sensors, fuel injectors, fuel pressure regulators, air filter, etc). If this is allowed to continue, it could cause damage to the catalytic converter as well.
If the smoke is blue, it means the vehicle is burning oil. This can be caused by bad pistons and rings, damaged cylinder walls, or other internal engine damage.
If the smoke is white, it is a sign of a coolant leak or coolant is being forced into the cylinders and burned. Typical causes of white smoke are faulty head gaskets, a cracked head, or a broken cylinder wall.