Simply put, you cannot.
On most Time Warner (and other) cable systems, cable channels are flagged as 5C "copy once." The PC is not a 5C authorized device, so it cannot record such content using the Firewire interface.
Other products, like HDTV D-VHS recorders and future HDTV Blu-ray recorders, are 5C authorized, so you can record all content with those devices.
For the most part, the only content not 5C flagged -- and thus, recordable with a PC -- is the local DTV/HDTV channels. Using your PC, you can create HDMV DVDs with high-definition content for playback on HD-DVD (but not DVD) players. Note however, that a dual-layer DVD only holds about one-hour of HDTV at ATSC bitrates. If you want to record more than one hour on a disk, you should start saving your money for a Blu-ray recorder.
There is one solution to record all HDTV cable channels with a PC, but that requires a Windows Vista PC with OCUR. You can read more about that right here
. Note however, that all recordings of 5C flagged cable channels with this solution are encrypted on your hard disk, so you can't send them to friends or copy them to DVD. As before, you can copy and burn content recorded from the local channels.