It's.... baby oil.
We read about this trick on a website a while ago and haven't yet tried it, but a family member swears by it. The baby oil isn't meant to clean dirt and grime off of the surface; you'll need to use a wet cloth for that. But once it's clean (and still covered with fingerprints), wipe on a thin coat of baby oil. The oil will erase the smudges and keep it shiny longer.
We've read about some people using mineral oil instead of baby oil; we'd imagine any type of oil would create that polished finish. But baby oil is easy to find and cheap.
Does anyone out there use this trick? Do you ever get a greasy feel? How does it hold up to fingerprints?