To register your TV to work with your Amazon Prime account go to the Amazon prime web page and login to your account and you should see a register device section.
Go to your TV and launch the Amazon prime app and you should be presented with a code to enter.
If you're using the Amazon Fire Stick then here's the direction for the Amazon Fire Stick.
- Select Settings from the Fire Stick TV menu.
- Go to My Account.
- Register your device: If your device isn't registered, a Register option displays on this screen.