Moving a waterbed asks for caution. A filled waterbed quickly weighs half a tonne. That is no detail.
Never with water in it
Never move a waterbed with water in it. The stabilising layers can shift, and the mattress will never be the same again.
Empty completely
Empty the mattress completely with a powerful pump while it still lies flat. Siphoning is not enough: the technique is not strong enough for the last litres and lets air into the water bag.
Folding
Then fold the head and foot ends towards the centre. You have three layers. Fold again across the width, six layers.
Storing
Store the mattress in a dry, clean, dark place. Avoid sharp objects. The longer the mattress stays stored, the more its lifespan decreases.