Fit your wet-dry vacuum with a fine dust collection bag. These bags are designed for the finer dust particles such as sheetrock dust.
Attach the brush attachment to the end of the wand and begin vacuuming the dust from the walls and ceilings. You may need several extension wands or a platform to put your vacuum on so it will reach the ceiling.
Wrap a microfiber tack cloth or other microfiber cloth to the end of a pole sander or other long pole. Other long poles you can use may include hard-floor sweepers that use detachable or disposable sweeping cloths.
Wipe down the walls and ceiling with the microfiber cloth and shake it out outside occasionally to remove built-up dust.
Wipe down the walls with a lightly damp cloth. Wring the cloth out as thoroughly as possible before use; it should barely feel wet to the touch.