Measure the distance from the ground to your dog's chest. This is the ideal height for the bottom of the dog door.
Mark this height on a wooden door.
Draw the outline of the rectangular dog door on the wooden door with a pencil, using a level to ensure that the lines are perfectly horizontal and vertical. The door should be large enough for your dog to pass through comfortably.
Drill a one-fourth-inch hole through the door at each corner of the drawn rectangle.
Cut the dog door out of the wooden door with a jigsaw, using the four holes to allow you to pass the blade through the door.
Cut wood strips to match the four sides of the dog door, which will seal any openings that have been exposed in the wooden door -- if the door is hollow. Glue the strips in place with weatherproof caulk and allow it to dry.
Re-measure the sealed dog door opening. Skip this step if your door is made of solid wood.
Cut a piece of one-fourth-inch plywood that is one-quarter-inch smaller than the height and one-eighth-inch smaller than the width of the dog door opening. This plywood will be the swinging door.
Sand it with 120-grit sandpaper to remove any splinters.
Place two hinges on the top edge of the swinging door and mark the positions of their screw holes with a pencil.
Drill holes through the plywood that match the diameter of the screw holes.
Bolt the hinges to the swinging door with half-inch bolts and nuts. The drum of the hinges should face away from the plywood surface.
Hold the swinging door against the opening, with its hinges positioned on the inside face of the wooden door. The top of the swinging door should be one-quarter-inch below the top of the hole to ensure it can swing fully both ways.
Mark the hinge screw holes on the wooden door with a pencil.
Drill one-eighth-inch pilot holes into each screw mark, then screw the swinging door in place using 1-inch wood screws.