What do you dial on your cell phone to make it a private call?

If you mean permanently, you will probably have to call your cell phone provider and talk to them. Because unfortunately you can get anyone's cell phone number off the internet. If you just want to block your number for a specific person you have to do that individually and with your phone and that varies with each cell phone. You will either have to call your cell phone provider and figure out how to do that with your specific phone or find your instruction booklet.