A showerhead that continues to drip even after the water is off likely indicates a dry or damaged washer. To replace it, turn the showerhead counterclockwise to remove it from the arm. Just inside the nozzle, there should be a small plastic or rubber washer you can swap out. Rewrap the arm tightly with plumber's thread-seal tape, working clockwise, covering all the threads to help tighten the fittings. Replace the showerhead.