Twist the ring piece on the shower head the sits on the pipe counterclockwise, using your hands. Continue turning the ring counterclockwise until the shower head comes free from the pipe.
Wrap a soft cloth around the shower head if you are unable to remove it by hand. Clamp a pipe wrench over the ring piece on the shower head, keeping the cloth between the wrench and the ring to prevent damage to the metal.
Turn the pipe wrench counterclockwise to unscrew the shower head from the pipe. If you still have problems turning the shower head, spray some penetrating lubricant into the joint between the shower head and the pipe, wait five minutes, then continue removing the shower head.
Peel off any Teflon tape or other material stuck to the threads on the water pipe to make installing a new shower head or reinstalling the old one easier.