Cut the door opening on one side of the hollow core door. Mark the door opening using the template supplied with the cat door. Drill 1/4 inch holes at each corner and cut between them with a jig or saber saw.
Drill holes through the veneer of the opposite side of the hollow core door from the inside aligning the corners with the corners of the first cut. Cut between the holes with a jig or saber saw from the outside of the door.
Measure the gap between the veneers of the hollow core door. Rip, cut lengthwise on a table saw, a piece of wood to this exact width.
Cut the ripped board into four pieces with two equal to the height of the pet door opening and two equal to the width of the pet door opening.
Place the pieces between veneers of the hollow core door. Hold in place, that’s the tricky part, while running a 1/2 inch screw through the veneer and into the ripped board. The ripped boards serve as a brace to hold the veneers apart and also as anchoring points for the door cat door frame. Run two screws from each side into each of the four pieces around the door.
Install the cat door in the opening according to manufacturer’s instructions. This usually involves attaching components of the door to each side of the hollow core door with a flexible segment hanging across the opening.