Answer:
It could be in a number of places. For most rifles, it tends to be on the receiver, while semi-auto pistols tend to have it on the slide. On some older rifles and shotguns, you may have to remove the plate off of the buttstock to find it. If you're uncertain of where to find it on your specific gun, you're better off to take it to a gun shop and have them locate it for you.
On military surplus rifles, especially those coming from the former Bloc states, the serial numbers may be on multiple locations throughout the weapon, such as the receiver, bolt/bolt carrier, magazine (on fixed magazine rifles), etc. Throughout their service life, many of these parts had to be replaced, and often these replacement parts were cannibalised from other rifles. If the numbers aren't all matching, it doesn't matter - the serial number on the receiver is the correct serial number.
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To add a brief note- many firearms do not HAVE a serial number. They were not required by law on rifles and shotguns until the 1968 Gun Control Act. Guns made earlier than that may never have had a serial number- and that is perfectly legal. REMOVING a serial number is not.