The tuner card connects to the pc via usb, the pc connects to the monitor via hdmi or vga or dvi (depending one what your pc and tv both support in common).
Since you mention a cable box then that would connect to the tuner card via coax and you would leave the tuner card on whatever channel the cablebox outputs (2,3, or 4 typically) You will need to install tuner software thats compatible with this tuner. It does come with their software that does work most of the time.
You will not get your encrypted channels and likely none of your HD digital channels as most cable companies encrypt these. You may get your local over the air channels if your cable company put them on the cable for free like they do here.
Be aware that that device will not work with windows 7, any edition. And Diamond has absolutely horrible support so dont expect a new driver... ever.