How do you find out the age of your vespa?

It should give the date of first registration on the vehicle registration certificate- however, it may not if the bike has been imported after being bought second-hand from overseas, or if it's been written-off and then restored. In this case, look at the chassis number, and then e-mail Vespa HQ in Italy- they should be able to tell you from the scooter model and chassis number what age it is. Their Customer Service section will be able to give you a reply in English, although this might take a little while.