Unscrew the gutters behind the existing fascia plate with an electric screwdriver. Then, place the brackets under the gutter to keep them in place and unscrew them so you can lift them up and away from the fascia. Remove the supports from the fascia channel so that they can be reused on the new plate. Remove the gutters from the areas where you are going to replace the fascia plate.
Common residential gutters are installed with long nails that secure the gutter to the face plate. To remove them, carefully detach the nails from the gutter with the lever or the claw of a hammer.