as tech warrior said, for the local channels, get a HDHomeRun (
link)
make sure they say "works with antenna" as some models are cable only.
there are different options, with different numbers of tuners, so pick what makes sense for you
get an HD antenna - go
here for help selecting an antenna, and seeing what channels will be available where you are
if you have cable service at the house (even if you're only paying for internet) you might be able to get the local channels off the cable, and not need the antenna, as a test, plug the cable into your TV, and scan for channels, see what you can find. it entirely depends on your provider.
the "works with antenna" should also work for pulling these unencrypted channels off the cable.
if you do have a cable subscription with TV channels, you can get the HDHrun prime, and a cable card from your provider, this will allow you to watch most of your subscribed channels on any device.
you will not be able to watch any fox owned cable networks (fox news, sports, Nat Geo, among others) or HBO
for me, showtime does work though.
The HDHomeRun will need to be placed close to your antenna or cable hookup, it also will need an ethernet connection back to your router.
on the aTV, get the "channels" app (
link)
this functions just like a cable box, you are able to select and watch live TV, as well as pause while you're watching.
if you want the ability to record programs when you're not home, or record one as you watch another.
there's a subscription option for channels ($8/mo or $80/yr), although you will need a computer with storage powered on all the time for this to work.
There is also a channels app for the phone (separate purchase from aTV app) that will allow you to watch live TV, or connect to the DVR if you've got that setup.
also with DVR subscription, you can connect to your home DVR with either the aTV or phone app away from home, if you've got the bandwith