If you have an internal capture card, you first install it into your computer, then you install all of the software onto your computer. With that, the A/V cables go into a reciever, which goes into the capture card, and you capture from your computer. To play on your tv, you can either split the signal of the video, or you can get some extra thing for the xbox cables which also has a S-video cable that can go into the CC's reciever.
External capture cards are pretty much the same, except it's outside of your computer, not inside

.