If you really want the full digital tier you'll need another cable box.
If your cable system uses Scientific Atlanta set top boxes (Time Warner and others), call them and find out if you can use the SA Explorer 8000 set top box. This is a full digital cable box with PVR (TIVO-like) capabilities and 80 Gb of disk. Tivo is far nicer (espec the channel guide) but the SA 8000 does a good job too.
On the gripping hand, most cable companies still support analog cable and don't bother to block the analog when a customer signs up for digital.
If getting the analog channels is 'good enough' for you, just hook the VCR up (to a split off the cable TV run) and run a channel search. You obviously will not receive any of the pure digital or premium/scrambled channels. But you may pull in the full range of basic analog. Even if that doesn't work initially you can always call the cable company to see if they can enable the analog channels.