A garden fountain is usually a stack of separate tiers with a pump and basin. Concrete and cast stone fountains are heavy and can crack, so drain everything, remove the pump, and move each tier separately on padding.
Pro tip: Photograph the tier stacking order and pump routing before disassembly so it goes back together correctly.
Watch out: Concrete and cast stone fountains crack from drops and flexing, so move each tier separately and keep them padded.