When removing a car battery, it is important to disconnect the cables in the correct order to avoid safety hazards and potential damage to the vehicle. The general consensus among the sources is to disconnect the negative terminal first, followed by the positive terminal. This is because disconnecting the positive terminal first can create a direct short to ground if the wrench slips. It is also important to avoid touching a metal object to both terminals of the battery at once. When reconnecting the battery, connect the positive terminal first, followed by the negative terminal.