Ok, first you'll need some sort of TV Tuner Card. You can find plenty all over; everyone has their own opinion. They range from ATI, WinTV, etc. to standard BT848 controllers & Conexant.
Then you'll want TV recording software. A lot of them come with WinDVR or PowerVCR II, but those are limited and kind of old; you might look into something like showshifter, etc.
If you want to output from your PC to your TV and keep HD type signals, you'll want a video card that either has SVid out (if your TV has) or DVI (if your TV has a DVI in) you will then want a program called PowerStrip. It will allow you to run your TV in custom resolutions designed for 16:9 HD, etc.
And if you want to record HDTV, you'd better get an HDTV card before July 1, 2005. All HDTV cards sold after this date will be crippled by Digital Rights Management (DRM), thanks to the FCC.
I wish I could help, but I don't have one of these cards yet. I'm still trying to figure out which one to get. I'm also still trying to figure out how I would test the thing, since I don't have very many DTV stations available in my area. (If it wasn't for the FCC Broadcast Flag thing, I would proabably wait a few years before even getting one.)
This post on the AVS forum has a lot of information about different HDTV cards, but hasn't been updated since 4/11/2004.
I added one of THESE to my new Medion PC and although I haven't hooked it up to TV signals yet, everything else about it workks great and the reviews are very favorable.
The Leadtek, based on the Brooktree (BT) chipset is pretty standard fare and well supported. There are tons of cards on the BT chipset, and the advantage is, all the right software supports it I alaso recommend Sage as mentioned above, neat software.