Simply put, you need:
a. An analog capture card to receive the TV signal. Note that this capture will be restricted to the 99 cable channel numbers normally obtained and will not necessarily include any digital channels. Of course, there is a way around that, but let's confine ourselves to the basics right now.
b. A splitter to split the cable signal into two components, one going directly to your TV or digital box...one going to your computer capture card.
c. A very large (more than 120GB) hard drive, if you intend to capture routinely. Capture files of video tend to be rather large before editing. SATA hard drives are ideal, but 7200 IDE/PATA drives work well.
d. A program to edit out commercials, if you are like me and cannot stand such
. If you are not going to edit, then skip this.
e. You need to decide whether you are going to save these captured programs...or just watch them and then delete them. If you are going to save them, you will need to increase your storage capabilities.
I have several analog capture cards, but I only use two: an AIW 9600 and a Haupaugge Win TV Go-Plus, http://www.hauppauge.com/pages/products/data_goplus.html
. I think I like the Hauppauge card better (fewer issues with drivers/software), but I tend to use the ATI AIW more now because I disconnected the other card (I have two desktops).
Going back to capture of digital stations...if you have a set-top box (I do), then capturing channels which are digital is easy. Rather than setting the splitter at the cable entrance, you merely place it at the point of output from the set-top box. When you want to capture from a digital station, you just set the computer card software to channel 3/4...and use the card like a VCR. The negative aspect of this is that the card captures whatever is on the TV screen at that time.
Analog capture cards are cheaper than cards which allow capture from digital sources.
If you provide the manufacturer and model of the card you are going to use, we can explore all your alternatives.