I hope somebody else has a better answer for you (I'd love to know it!), but I have been hired to do post-remodel cleaning and I've a method, but no quick and easy tricks. The darn dust is so fine, that it gets into and onto everything.

I start by removing any cloth that can be removed and taken outside to shake like heck and left hanging while I finish up inside. Begin high, dusting every ledge, molding, ceiling fan, fixture, the tops of cabinets etc. I have a tool that looks like a dry mop, but has a short handle. The rag mop head can be misted with just a very little bit of water or very dilute Murphy's oil soap to help it move dust off surfaces rather than simply pushing it around. A feather duster really doesn't do for this kind of dust as it does little more than send it airborne.

Do this upper dusting in each room, and then return to the first room to dust the middle surfaces. Then do the same circuit to dust lower surfaces. The circuit method allows time for the dust you've stirred up to settle down on the next level under the one you just dusted.

At the finish, you vacuum upholstered furniture and floors and then mop floors. And realize that you will still have a certain amount of dust, it's unavoidable. But this method, if you're careful to dust every surface, you'll get the worst of it.

Dusting the walls is the worst for me, as it's tedious, but is generally only really necessary in the specific rooms where the remodel occurred. Yes, you'll have a certain amount of dust on the walls in other rooms, but it will slowly sift down and be dealt with in your normal cleaning routine.

My advice, really? I know that having just spent what is probably a lot of money on the remodel, spending more hurts, but hire a professional to do it for you. Many contractors know people to refer (that's how I get these jobs, though I try not to do too many of them as it really is more work than I care for). Budget for two visits, about a week apart. You may decide after the first visit that you can live with the remaining dust level until it is taken care of by your regular cleaning routine, in which case you can cancel the second.

Do this only after your contractor is completely done doing anything that would involve cutting tile or making holes in the ceiling/walls for fixtures etc, or you might just have to do it again.

IMO, a steam cleaner or a vapor cleaner (I have one) is not the solution. They are good at removing dirt that is stuck on floors and walls, not dust that is being blown around.

You might want to try posting this message on the Remodeling forum to see how others have managed this situation.

Here is a link that might be useful: Remodeling forum