A normal cough usually last at most 18 days.
If your cough is persistent and doesn't go away on it's own within 18 days you may need to see your doctor about the cough to make sure it's not caused by something more serious than just a natural cough.
You can try getting rid of the cough by adding moisture to the air with a vaporizer or humidifier or even take a hot steamy shower.
Also taking Halls cough drops seem to help me get rid of a cough as well as Vicks Vapor Rub on my chest.