Most colds go away on their own within a week or ten days as long as you get plenty of rest, stay hydrated and take some cold medicine.
If the cold last longer than 10 days then you could have a more severe viral infection and after 10 days I would see a doctor just to be sure it's nothing more serious as in a more serious viral infection or some other infection that needs antibiotics.
However for just the common cold there's no cure and nothing much a doctor can do about it unless it lasts longer than 10 days or the cold seems to get worse.