The directions for accessing Prime on a Sony TV state that one should click 'Home' on the remote, go to 'Apps' and then add Prime. However, my remote does not have a 'Home' button nor can I see an option on the TV for 'Apps'.
You need to download the Amazon Video app and register it to your account. If you already have the app, register it to your account.
to download the app, if you do not have it, consult your TV manual to find out how (Google is very good on such things)
Have you looked at:
If your tv is not a smart tv, or is more than a couple of years old, you may need a fire tv stick or other device...