You get a TV capture card and connect it to your computer. Connect the Video Out on the cable box to the capture card. Then either connect the computer to a serial connection on the cable box (only if it's supported) or use an IR blaster to have LinuxMCE control the cable box. Then you can output to your TV using whatever your TV supports. Some TV's support VGA, DVI, HDMI, S-Video, Component, etc. It all depends on your TV and computer video card.
I'm pretty sure this is all explained in the Wiki...