How do I open the app on my smart tv?

Select newer smart TVs support the Apple TV app. See if your TV is among those models. Apple TV app-supported smart TVs and third party streaming devices - Apple

Other TVs would not support the app, and would need a HDMI-connected streaming device, such as the Apple TV box, a Roku or Fire TV, or select gaming console. All the ways to watch Apple TV+ - Apple Support