When replacing a car battery terminal, start with the negative terminal first. This reduces the risk of short circuits or sparks occurring while disconnecting the positive terminal. Disconnecting the negative terminal first breaks the electrical circuit and reduces the chance of accidental shocks or damage to the electrical system. After replacing the negative terminal, proceed to replace the positive terminal. Always ensure to follow safety precautions, such as wearing protective gloves and eyewear, and double-check that the ignition is turned off before beginning any work on the battery terminals to prevent accidents and ensure proper installation.