Before changing a bulb in your electric fireplace you should always turn off the electrical supply to it.
An electric fireplace will be connected up to your home electric in one of two ways:
Electric fireplaces are more commonly supplied with a power cable and plug, and simply plugging them into any one of your standard electrical outlets will allow the fireplace to work straight out of the box.
If your electric fireplace is plugged in at the wall be sure to turn the fireplace off on the unit itself and unplug it from the wall before attempting to open the fireplace to change the bulb.
Electric fireplaces that are more of a permanent solution in a home, such as installed within an entertainment center or within a wall, may be hard-wired into the house electrics.
If so then you’ll need to isolate the power to the fireplace. The easiest way can be to manually trip the fuse inside your fuse box that supplies power to it.