Its the same thing as buying a new phone. Just that it looks a little different. Can you watch TV if you buy a new phone?

If you buy a vanilla Android TV box, you would need to install the apps you want to watch something. Some boxes come "pre loaded" with apps that allow you to watch content. Assuming they even work.

There's a bunch of ways to consume content. Both legit and non legit.

I use my Shield with an OTA antenna connected to a HDHomerun, the rest is online services: my national broadcaster, netflix, youtube, etc. I dropped from 165$ / month for three services ( internet / phone / cable ) to only 57$ / month ( internet and phone)

my shield paid itself a number of times. best investment ever

Android TV comes in various forms, mainly televisions (which can use a coaxial cable, so yes you can get cable or over the air signal on them), and boxes which you connect to a television using an HDMI cable (these usually come without coaxial cable connection).

The main ways in which people watch content on them are Youtube and subscription services like Netflix/HBO/Amazon Prime/etc.

You can attack USB and Network and IPTV tuners, these tuners allow the Live Channels app to show you TV channels in its interface, some USB tuners known to work with Android TV are the Hauppauge WinTV-HVR-955Q and the WinTV-dualHD, network tuners from Hdhomerun also work with Live Channels and finally IPTV tuners are applications that you can install from the Play Store and show their channels on Live Channels, some of these apps are Haystack TV for random news and TVirl for your own custom .m3u playlist, this last one TVirl app is GREAT if you know what you are doing.