Welcome to the forums from the Wiregrass, JD! The official serial number is located on the butt of the grip frame. If your M29 has grips that cover the grip frame (e.g., targets, combat, boot), you need to remove them to see the serial. Some later models also have the serial stamped on the frame above the yoke hinge. If you give us this number, we can tell you approximately when your gun was made. We don't need the whole number, just the first 3 or four and any single alpha prefix or, for more recent guns, the 3 alpha prefix. We do need to know the total number of digits on earlier guns. So, you can XX out the last two or three numbers if you are concerned about privacy.
I see Abby's Dad beat me to it. JD, the model number is stamped in the yoke area and you should be able to read it as MOD 29-? with the cylinder open.
It is believed the first Model 29 marked gun was produced early in 1958. They stopped making Model 29's in 1999 with the exception of smaller numbers of them. If like other S&W's look on the bottom of the grip frame.