That will depend on the make of the rifle and the age of your pump rifle.
Old gun catalogs
Basically impossible to do with just the serial number.
It is likely that a Savage Model 22 rifle does not have a serial number. Serial numbers were not required by law in the US until 1968.
With the serial number that you supplied,your Winchester model 1894 lever action rifle was produced by Winchester in the year 1972.
top of barrel
Should be on the barrel near the receiver.
You will need to include the model number to your question to find a answer.
Buy supplying the model of your rifle and the serial number.
What is the year of manufacture of Winchester model 94 rifle serial number 2359141
No such model number