I use several trashcans, a lot of freshly mixed seawater, and several styrofoam coolers to transport everything. All fish, motile inverts, and relatively small, loose corals go into individual bags. Attached corals go in a cooler that is filled, while live rock goes into a cooler with some damp newspaper and/or paper towels. Leave the sand in along with a tiny bit of water over the surface.
That being said, I have only had to move my own stuff once, but I have moved numerous other tanks as part of an aquarium maintenance program and/or for friends. BTW, this method usually works out quite well, especially over shorter distances.