So how is it done then?  
This is the antenna that I have mounted to my roof:

I get about 60 channels, though some of the farther ones have spotty reception; I'd say a couple dozen are consistent and reliable.  Of those, roughly 1/3rd are HD.
Most HDTVs have built-in digital tuners, but in my case, I use a device called a 
HDHomerun that connects to my antenna and plugs in to my network.  With that, I can watch broadcast TV from any computer, newer game console, HTPC, tablet, or phone connected to my network.