If you have a cable box, I think you'll need to hook that up to your TV card and just leave the tuner on channel '3' or whatever, and change channels with the cable box.
If you only have 1 cable box, you'll need to get another from the cable company (usually only a few bucks more a month)
You won't need to have another outlet unless you want to- you can just split the signal from the first outlet. If you do want a new outlet run, I don't know how much they'll charge you for it.
If you want to hook up a VCR to the computer, do what was already suggested. If you have a cable box, it will have to be hooked up like this: Cable Box -> VCR -> Computer. And it was suggested that if you want this hook up, you don't even need a video card with a coax in, just get one with a video in, and hook up the VCR via an RCA cable.
phatty