Wrap the shower in moving blankets and strap them on so they don't slip off. This will decrease the risk of damaging the shower in transit
Tilt the shower slightly back, just enough to get the lip of a hand cart underneath it. Slide the hand cart all the way in until it is pressed against the side of the shower.
Tilt the shower toward the handcart slowly and carefully. With helpers supporting the shower and keeping it from tilting to far in one direction or the other, begin rolling it. Keep the center of gravity of the shower directly over the wheels.