Most cable boxes, if not all, can be used with TiVo.
You feed the cable output into the TiVo instead of into the TV.
You set up your TiVo by identifying your local cable company and your level of service, if you have a cable box, and if so what type of box you have.
The TiVo will need to control the cable box where channel changes are concerned, and so it has to know what type of box you have to identify which control codes it should use.
The TiVo can control the box by two different means. One's a "serial cable" that plugs into the back of the TiVo, with the other end plugging into the back of certain cable or satellite boxes. It's a hard wire connection, so very little chance of bad channel changes happening because of the box "misunderstanding" the command.
Unfortunately, not many boxes will work and play nice with the serial cable.
That leaves the other option, an "IR blaster" or "emitter".
You also plug this into the back of the TiVo, and the other end, sort of like a flashlight, gives off the same type of invisible pulses a remote control would give off.
You put the blaster in a spot where the cable box can "see" the IR flashes, and when the TiVo tells the box to change channels, it does.
Sometimes for different reasons the signal is misunderstood by the cable box, and you get "Nova" on PBS instead of "The King of Queens". (The box changed to the wrong channel.)
The best thing to do if you see this happen is build a "fort" for your cable box. Put it into an enclosure where no light can reach it, but at the same time try to make sure it has some ventilation. Put the blaster in there too, in a spot where the pulses from it will be seen by the cable box's sensor.
Your channel changes, controlled by the TiVo, will be as accurate as possible.
No sidewalks with beef, please.