You need a reversing ring with a 52mm thread on one side and a standard Nikon lens mount on the other. You screw the reversing ring thread onto the filter thread at the end of the lens, then attach the lens-mount side to the camera body. You would do this with your 18-55mm lens because:
A) I believe the 18-200 has a 72mm filter size and
B) A wider angle lens gives greater magnification when reversed, so the 200mm is unnecessary anyway.
As your lens does not have a manual aperture ring, you will need to hold the aperture lever open at the exposed end of the lens (the end that is normally attached to the camera), either with your finger or with a blob of poster tack. You then set your camera to manual mode to start taking photos, as this mode ignores the lack of a CPU connection.
See the Photography StackExchange Blog post on reversing rings which tells you everything you need to know to get started, here.