Remove the panel of the pool enclosure screen in which you plan to install the pet door. Place it on a flat work surface such as a table, with the screen spline (the rubber strip holding the screen in place) facing upward.
Place the pet door in one of the bottom corners of the pool enclosure screen. Mark the length and width along the screen border. Pry up the spline in this corner with needle-nosed pliers and pull off to both the length and the width marks. Fold the spline out of the way and pull back the screen in the corner.
Slide your pet door into place in the corner, over the frame of the pool enclosure screen. Make it flush with both the bottom and side of the frame, pushed securely against both.
Install the screws that came with your pet door kit through the pet door frame and into the screen frame, using a drill to create starter holes if necessary.
Pull the screen material from the corner of the pool enclosure down over the pet door making it as tight as possible. Hold the screen in place around the pet door by using a flat-head screwdriver to press a strip of screen spline in place along the two sides not touching the frame.
Cut the excess screen away from the pet door with a sharp utility knife to finish the installation process. Place the pool screen enclosure panel in its former location.