First, whether or not you can do this will depend on cable box useage, and how the VCR is hooked up. In the earlier days of cable TV, & off-air reception, this was a simple task.
If you have a satellite receiver box or cable box which is used to tune the channel, rather than using the TV itself or the VCR tuner, then recording one channel while watching another may not be possible. While I don't know the capabilities of newer sat/cable boxes, older ones sent just one signal out to the external equipment (TV etc.) That one signal (channel) is all that is available. If you received a manual with the sat/cable box, see if it says anything about this issue.
That being said- if you don't use a sat/cable box, but instead use your TV or VCR to select the channel you are watching, then assuming the VCR is hooked up inline with the TV, just setting the VCR/TV option to TV will pass all channels through to the TV, and you can then use the TV to select whatever channel wished, while the VCR is recording something else.
Hopefully I haven't confused you. If another contributor has some additional info on the capabilities of sat/cable boxes of today, please read their contribution.