You have round metal plug on the side of the engine its self that has its identification information. If this is a new to you motor and the identification plate on the transom bracket is missing and the identification metal plugs is missing on the motor itself, then you may have a stolen motor. If I am not mistaken, it is illegal in most states to have an outboard without any identification due to anti-theft laws.
If you find the number on the plug or bracket, here a link to tell you its year make or post a picture of the motor and someone should be able to identify it or a very close year guestimation.