There should be a manufacturer label on back or side of your computer (or bottom in case of a laptop), this should have the serial number information which helps the manufacturer track information about its production and sale. Typically it will have "S/N:" before the start of serial number. It is different from the operating system license number or product key which is on computers with Microsoft Windows.
However, the easiest way of finding the serial number is the following:
Run Command Prompt by typing "cmd" (without the quotes) in the search bar and hitting enter.
Type in the following (again, without the quotes): "wmic bios get serialnumber"
Make sure there isn't a space between the words serial and number. Hit enter.
It will output two lines, the first will say "SerialNumber" and the next line will have your serial number on it!
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Dell uses tag numbers or service numbers located on a small white sticker with a bar code on it. This number is used by dell to identify your specific PC.
If you are referring to the Windows product key, then it should also be a greenish sticker with a 25 digit number.