Look on the box that your appliance came in -- if it is a smaller appliance, such as a coffee maker or a compact refrigerator. This box typically contains information about your specific appliance such the name of its manufacturer and other types of product information. On the identifying label on the box will also be the year your appliance was manufactured.
Find the identification label printed somewhere on the appliance itself. On this label will be the model number and serial number of the appliance, as well as a copyright date. This copyright date reflects the year your specific appliance was manufactured. If your appliance has more than one copyright year printed on this label, the most recent year is the one the appliance was made.
Flip through the instruction manual that came with your appliance until you find the "Technical Specifications" page. The year your appliance was manufactured will be printed on this page as well as other technical information about the product, including warnings about its use and other types of power and performance information.