Moving expensive works of art

Depends on what kind of work. Paintings are typically shipped in large, flat crates, painted side up (because some media are prone to flaking/dusting off bits of pigment.) Wrapped in padded, quilted blankets, typically, within the crate.

Sculpture, glass, and pottery are different stories and use different methods.

A friend of mine told me he was doing work at a house, well, actually it was a mansion, and the owner had a painting delivered. It was sent in a refrigerated truck and packed inside a crate. It was an extremely expensive painting.

Adding a link: Smithsonian Office of Exhibits Blog. They talk about the behind the scenes of setting up an exhibit. I believe they've had some commentary on moving the art.