First go over to Sugarhill's fine post on hooking up your TV with your computer and then come back here! (unless you're rocking a laptop, then no need, unless you want a bigger screen)
Once your have your desktop configured, or if you have a laptop you'll need a couple of things before you can DVR over the air tv for free. You can run your cable through your computer, but that's like blackbelt level tinkering and mrchien did that in our house. I know how to get the free stuff! ;)
Before we go any further, if you're running Windows 7 you're golden! Simply boot up Windows Media Center and start poking around. If you're on Win 8 bad news folks, you have to pay for the Media Center :( Although I'm certain there are other programs you can use. But for simplicity, today's demo is going to use Media Center, cuz that's what i know best.
The first thing you'll need to acquire is a TV Tuner, i prefer the USB versions with the option to put on an electric antenna (for better reception) and a remote control. You can also purchase a remote separately, or if you need the exercise, you can use your mouse. :)
Next install the Tuner and make sure it's working (i'd give instructions, but each manufacturer is a bit different). Don't forget to attach the antenna!!! I prefer to use one with a power source because i get in more channels, but simple rabbit ears will do too. Once done boot up Windows Media Center. Next head find the Tasks/Settings tab, once there you're going to click on the one labeled "TV" from there it should ask if you want to set up signal, click YES! And this should be pretty self explanatory. Don't be afraid to play around with it, worst case scenario is you have to reinstall the thing, or worse, rescan to find the channels!!
You can also use this as a DVR too, just keep in mind that these files are large and can take up a lot of space on your computer's hard drive. I use an external hard drive just for my tv addiction. Bonus, i can simply bring my unwatched programs with me when on the road!
Oh, but how to DVR?!? Go back into Setting, click on TV and the click on Recorder and go play with the settings until you get them how you like them. (i'm a 5 min before and after gal, cuz shows don't always end on time!) I access and set my recordings through my remote, but you can also right click with your mouse to when watching a program to set it to record. You can also scan the program listings and set up programs to record while your gone or if you're going to watch another show at the same time.
If these directions aren't clear enough for you, cuz sometimes i'm not the best writer, you can find the official ones here :)
As i said earlier, I'm not that great at at this kind of writing, so please feel free to give me kind suggestions or questions so I can edit this post to be more helpful!