Turn off your electric fireplace. Wait for at least 10 minutes for the bulbs and fireplace to cool.
Unscrew the screws securing the doors to the fireplace to remove the cover or doors. Some free-standing models require turning the entire unit around and removing a back access panel. Read the user's manual to determine how to access the bulb assembly.
Lift the logs and grate out of the fireplace. You may need to remove the fireplace trim before you can take the logs out of the fireplace.
Rotate the burnt-out bulb counterclockwise to remove it.
Install the new bulb by turning it clockwise.
Reassemble your fireplace. Reverse steps 1 through 3.