Electric fireplace inserts can typically be removed by pulling the unit towards you out of whatever it has been placed within, such as an existing fireplace.
When removing an electric fireplace insert take into consideration that the unit is likely to be plugged into the electrics somewhere behind.
By partially removing the electric insert you can check to see where this electrical connection is.
For example, the power cord for our electric insert can be seen on the side of the back of the appliance when partially removed.