There are a number of sources for finding out the date your home was built.
Your ownership documents: title policy, previous title searches, deed history, purchase appraisal
Your county offices: Your county recorder or tax assessor will have these records. Depending on your county you can look them up online, call them, or go to their office.
Public listing websites: Websites such as Zillow may have a build date listed for your address, although, this is not a verified source and is not always accurate. The best way to get accurate property information is to refer to your homeownership documents or to contact your county.