digital cable isn't like the old fashioned analog TV.
Back then a splitter could solve most problems.
Today's digital cable requires special boxes, which must be activated by the cable company. You can't just go out and by a digital tuner and have it work.
Like MDS said, if all you want is the bottom tier analog channels it's not a biggie, but if you want the premium channels, you're gonna have to play their game.
In my humble opinion, if you want record the premium channels, I suggest you simply bite the bullet and rent one of the cable companies diskless recorders.
Your only other alternative is to connect the red/white/yellow outputs from the cable box to the aux inputs on the DVD recorder, tune the cable box to the channel you want to record, leave it on, set the DVD recorder to start and stop at a certain time, and make sure it's set to record from it's aux inputs. You won't be able to watch one thing and record another, though.