A parabolic listening device is really just a fancy name for a shotgun microphone. A shotgun microphone is a device that can pick up sounds at a distance when you point it at what you want to hear. A hemisphere- or parabola-shaped reflector catches sound from the chosen direction and focuses it on a microphone, amplifying a sound which would otherwise be too faint to hear.
Cut the horn off of a small satellite dish using a hacksaw or other cutting tool. The horn is a small detector suspended above the surface of the reflector by a pole.
Position a vocal microphone so that its screen is right at the spot where the horn used to be. You may have to cut off part of the pole to get the mic positioned right. Attach the mic to the rod with epoxy to hold it in position.
Tape a small headphone amplifier to the back of the listening device. Tape the microphone's cord to the rod holding it in front of the dish, and plug the end of the cord into the headphone amp.
Plug in headphones and switch on the amp. Point the parabolic listening device at whatever you want to hear.
You may want to attach the microphone with duct tape so that you can adjust it to get the perfect position before epoxying it. If you can't get your hands on a used satellite dish, use a salad bowl, umbrella or anything else roughly parabola-shaped. Use a stick to hold the mic out in front of it.