You will need the set-top box, make no mistake about that. If you are smart, you will get two (one for TV, one for computer).
Simply put...you run a coax cable from your DTV converter box...to a TV tuner card which is installed in your computer.
Example: I have a tuner card in each of my two PCs...and I have cable courtesy of Time Warner.
I have the cable connection coming from the wall...I connect that to the box (which I need to receive any channels beyond the basic 125 which are basic cable). I can receive the 125 without the box, straight from the wire, but I need the box to receive any channels which are above 125 in the numbering system. This is standard.
Back to the box
. The box, in addition to regular and tiered cable channels, will also pick up free and paid digital HD channels. The key is what you subscribe to...no subscription, no capture via the box.
OK, so we have the cable to the DTV converter box. Now I need to connect another coax cable to the output from the box...and I can now I connect a splitter to the coax. I use a 2-way splitter (readily available at Walmart, etc.) to give me two possible connections from the one coax cable. One connection for my LCD TV...one connection for my tuner card in my PC.
Based on my experiences, it is considerable smarter to just pay for another converter box (I pay $3 a month for mine) and use the splitter back where the coax cable comes from the wall. Then run another coax cable to the computer system/tuner card, while running the other splitter lead to your TV.
The tuner card for the computer...will have its own software for setup/tuning, etc.
FWIW: Get a PCI-e tuner card.
The reason I suggest two converter boxes...if you try to use only one for two outputs, both the computer and the TV will reflect whatever is reflected on the one box. Duplication is not the goal, so get two boxes and you will have two differing views from the same cable signal.
Hope that helps