I can't find a way to sign into my tv with my new subscription of appletv

The Apple TV app is available on select smart TVs and select TV-connected streaming devices. If your device is supported, then you may have the app pre-installed, or you may get it (download it) from the on-device App Store (Play Store/​Content Store/​Channel Store).

List of Apple TV app-supported smart TVs and third party streaming devices - Apple

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

All the ways to watch Apple TV+ - Apple Support

Once you have the Apple TV app on your device, then you should sign in to the app, through the in-app Settings (sprockets wheel icon), with the Apple ID account that has the subscription.