How do I get my free 3 month subscription of Apple TV to work on my smart TV?

First see if your TV supports the Apple TV app.

List of Apple TV app-supported devices - Apple

If your TV is not listed as compatible, then you may need to connect an external streaming device. An Apple TV box, or one of the third party streaming devices as listed in the above linked document.

All the ways to watch Apple TV+ - Apple Support

Get the Apple TV app or Apple TV+ app on your smart TV, streaming device, or game console - Apple Support