Unfortunately you can't AirPlay it via appletv, as the AFL deliberately blocks this, so you get audio only. Presumably this is so they can sell both digital and pay TV rights without them competing.Yeah, I've got an iPhone, so should work ok if I hit the play button on the green headphones and use AirPlay to put it through my AppleTV... correct?
To see it on your TV, you can plug your phone in directly using a Lightening/HDMI adapter. Or you can mirror it via appleTV, so you see your whole tablet screen, not just the app. But in my experience this looks worse, as it doesn't fill up the whole TV screen and it's too small to be clear.