How do I watch Apple on my television at home?

See >>> All the ways to watch Apple TV+ - Apple Support

In summary, assuming that you have an active AppleTV+ subscription, you can watch AppleTV+ from:

• Your Apple devices using the AppleTV App
• Using your Apple devices - connected to your TV via an HDMI Cable
• Using your AirPlay/Airplay2 to wirelessly stream content to an AirPlay compatible TV
• With an AppleTV box, connected to your TV

Has your AppleTV box been updated to TVOS 14.4? If so, assuming that you are signed-in to iCloud with the AppleID to which your AppleTV+ subscription relates, you’ll be able to watch content directly.

Otherwise, you can use AirPlay to play content from your iPad/iPhone/Mac.