On your Mac, click on the Apple icon in the top left of your screen, then select “About This Mac”, then double-click the version text, for example “Version 10.9”. You will see your serial number where the version number used to be. Alternatively, select “More Info” to see your serial number.
On a Dell, use the “Dell Service Tag Number” which is on a label both on the top and back of the machine. It is a mix of numbers and letters 7 digits in length, like “47S4KS1”