If you have an upright piano, please consult the following diagram:
If you have a grand piano, the most common place to find the serial number is underneath the music rack. Try to removing or sliding the music rack to expose the gilded plate underneath, then consult the following pictures to help you locate the serial number.
Sometimes the serial number is stamped on the soundboard underneath the strings.
Kimball pianos may have a specialty location behind the keybed. This is looking from the tail-end of the piano.