The question can't be answered without knowing who made it, what caliber/gauge and whether it is a revolver, semi-auto, rifle or shotgun.
By the serial #
You are going to have to identify the model number to determine the age. Take the gun to a gun shop or gun smith for assistance.
By the serial number.
1971
Where did you get that gun?
Serial number tables, if published
The model number of the gun and make along with the serial number usually will determine the age of a gun.
This gun was made in 1952
Find books on the maker.
1977
The letter of the given serial number indicates the year the gun was manufactured. In this case, the gun was made in 1960.
4092