It depends... What model do you have, is it New or Used and when did you buy it?
If it's new and it came with an envelope containing a spent shell, the test fire date written on the envelope is within a week of it rolling off the line. This is close enough for most.
Depending on the model (and when it was made) there's either a 4-Digit code on the label (between the 2 bar codes) consisting of the last digit of the year and the number of days into that year (ie: 2123 means 2012 - on the 123rd day) or (like Shields made this year), a 6 digit code to indicate either MMDDYY or YYMMDD (I don't remember which).
Hope this helps some.