Depends entirely on your car make and model. On many models you can disconnect or remove the fuse for the telematics control unit (TCU) and it's as simple as that. However you won't receive any OTA updates that will likely solve problems. And if you reconnect to get them, there's no guarantee your car doesn't suddenly dump all your personal data obtained in the meantime onto company servers. Further I find it more and more likely that OEMs either already have or will add a ToS that requires you to keep all this stuff connected, and they'll argue that the data collection is part of the sale.

Slate seems to be the only brand currently that intends to deliver vehicles with zero connectivity required.