Clean, dry, soft cloths or feather dusters will effectively remove dust; however, to avoid scattering the dust into the air, where it floats until landing back on furniture surfaces, dampen the cloth very slightly.
Start at the top -- dusting the ceiling, ceiling fans, and ceiling lights. Work your way down the walls and onto the furniture. Don't forget books, house plants, and blinds.
If possible, take house plants outside and blast them with compressed air.
Finish it off with a vacuum and you'll be breathing easier in no-time.