Use a measuring tape to determine the circumference of the plastic fence post.
Wearing gardening gloves, measure a length of wire equal to the circumference of the fence post plus six inches. Cut it with wire cutters.
Make a pencil mark on the back of the birdhouse halfway between the base and roof.
Hold the piece of wire you cut so that the center of it covers the pencil mark on the back of the birdhouse. The wire should be horizontal--parallel to the base of the birdhouse.
Position the staple gun over the wire at the pencil mark, holding it so that the sharp points of the staple will be inserted on either side of the wire. Squeeze the staple gun, stapling the wire in place at the pencil mark.
Apply a second staple about 1/2 inch to the right of the first one and a third staple about 1/2 inch to the left of the first. If the wire feels at all loose, add some additional staples.
Mount the birdhouse by holding the stapled part flat against the plastic fence pole. Bend the two ends of the wire around and to the back of the pole, then tightly twist the two ends around and around each other with the pliers. Wear gardening gloves to help you get a tight twist and hold the birdhouse steadily in place.