The dust is probably plaster and / or concrete dust, and as such will be heavy, fine, and annoyingly hard to shift.
(1) Wipe down vertical surfaces initially with a dry cloth, and sweep up as much as possible.
(2) Wipe down vertical surfaces with a slightly damp cloth (I've seen suggestions for dampening with white spirit for units and tiles which may remove any other grease / residue traces as well. Don't use white spirits on painted walls, though - don't even wipe those down with a damp cloth unless you know the paint is water-resistant), brush floors etc with a sweeping brush covered with damp cloth.
Be very careful of the walls - if you haven't had them painted yourself / to your specifications, chances are it's just at builder's finish first painting, and the paint generally isn't great. Usual recommendation is to have them re-painted in a year to 18 months, by which time the house should be fully dried out and any emerging surface imperfections can be dealt with.
(3) Bulk of dust should be gone by then (though other posters are right - some more may continue to settle for a few weeks, depending on when the builders left), walls should be ok, clean as normal - use whatever floor cleaner you're recommended for the floors, sponge down units, tiles etc with a mild detergent solution (couple of squirts of washing up liquid in a basin of warm water) and dry.
And congratulations on the new house!
