Lock the jaws of a pair of vise grips over the shower arm, 4 inches away from the shower wall. Hold the shower arm between the wall and the vise grips with one hand to prevent pushing the inside plumbing pipe. Rotate the shower arm counterclockwise with the vise grips, and remove it from the shower wall.
Wrap plumber's tape around the threads on each end of the new shower arm. Wrap the tape in a clockwise direction to prevent the tape from unwinding when attaching the shower arm and shower ahead.
Thread the end of the shower arm into the pipe in the shower wall until it is hand-tight. Place a cloth over the shower arm and lock the vise grips over the arm and cloth. Rotate the arm clockwise until the opposite end of the arm is pointing toward the tub or shower floor.
Screw the new shower head onto the end of the shower arm until it is hand-tight. Move the cloth from the arm onto the shower head connection and turn it another three-quarter turn with the vise grips.