Disengage the furnace and air-conditioning systems. Air should not be circulating while you are cleaning the vents.
Work from the top floor down so that any dust accidentally pushed into the duct work will float down eventually getting cleaned out at the bottom most grate. Proceed to the uppermost floor of the building and locate the vent grate. Remove the grating by unscrewing any fasteners. Vacuum both sides of the grate with a shop vac. Depending on the style grate a small brush attachment may work best.
Inspect the angle of the duct work. If it goes straight for a considerable distance, attach a long nozzle to the shop vac's hose. If the duct turns, then you will need to fish the hose itself into the duct. Turn on the shop vac and clean out as much dust as possible as far into the duct as you can reach the hose.
Wet a sponge and wipe the duct clean. The shop vac will leave behind small particles of dust that a wet sponge will easily remove. Wipe down both the inside and outside of the vent grate as well.
Replace the grate and continue this process working from the top floor to the bottom.
Replace the filter on your furnace, air-conditioning unit or HVAC system. Do not turn it back on for an hour to ensure any dampness from washing has evaporated.