Two ways that I learned of from this board. (1) Someone with a S&W catalog may come along and using the serial number give you a probable year of manufacture. (2) You can call S&W customer service and they can tell you from the serial number. That is what I did with my two Smith semi autos.
You have a fine model of a 3d generation semi-auto. If it is in good condition now and properly taken care of, you will be able to pass it on to your children or grandchildren. It is a great example of fine American craftsmanship.
Enjoy it safely.